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Risk sensitive reproductive strategies

The effect of environmental unpredictability

Bård-Jørgen Bårdsen

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ABSTRACT A crucial task in ecology is to quantify trade offs between competing demographic processes for experienced by individuals that inhabit unpredictable environments. Perhaps the most widely studied trade off is that between current reproduction and future survival (‘the cost of reproduction’). While experimental studies have been widely used to quantify life history strategies in birds, virtually no experimental studies have been carried out on large and free ranging mammals. This thesis quantifies how female reindeer Rangifer tarandus subject to variability in food availability, trade their resources between reproduction and body mass to ensure own survival. By combining two experiments, one observational study and one theoretical model, this thesis show that: (1) Individuals subject to reduced food availability in one winter feeding promptly reduced their reproductive allocation the following summer to increased their autumn body mass. On the other hand, short-term improved conditions did not result in increased reproductive allocation. (2) Long-term improved winter feeding conditions did, however, result in increased reproductive allocation. (3) Reproduction was costly, especially for smaller females, as occasional harsh winters and high population density resulted in reduced reproduction and lowered female body mass. Moreover, a successfully reproducing female produced a smaller offspring in the coming year relative to a barren one. Reindeer also differ in their intrinsic quality as successfully reproducing females’ showed an increased probability of reproducing also in the following year. (4) In harsh and unpredictable winter conditions, the optimal reproductive strategy involved a low reproductive allocation per unit female spring body mass. Under such conditions females increased their autumn body mass to enhance their own survival. Conversely, the optimal reproductive strategy in benign and predictable conditions involved a higher reproductive allocation. (5) Reproductive strategies and environmental conditions had significant effects on population dynamics. Female reindeer do not to jeopardize their own survival and adjust their reproductive allocation in order to buffer periods of low food availability in a risk sensitive manner. Key words: cost of reproduction; evolution; environmental stochasticity; phenotypic plasticity; Rangifer tarandus; risk sensitive life histories.

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PAPERS INCLUDED IN THE THESIS Paper 1 Bårdsen, B.-J., P. Fauchald, T. Tveraa, K. Langeland, N. G. Yoccoz and R. A. Ims. 2008. Experimental evidence for a risk sensitive life history allocation in a long-lived mammal. Ecology 89:829-837. (doi: 10.1890/07-0414.1) Paper 2 Bårdsen, B.-J., P. Fauchald, T. Tveraa, K. Langeland and M. Nieminen. in press. Experimental evidence of cost of lactation in a low risk environment for a long-lived mammal. Oikos. (doi: 10.1111/j.1600-0706.2008.17414.x) Paper 3 Bårdsen, B.-J., T. Tveraa, P. Fauchald and K. Langeland. manuscript. Observational evidence of a risk sensitive reproductive allocation in a long-lived mammal. Paper 4 Bårdsen, B.-J., J.-A. Henden, P. Fauchald, T. Tveraa and A. Stien. manuscript. Plastic reproductive allocation as a buffer against environmental unpredictability – linking life history and population dynamics to climate.

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PREFACE This study was financed by the Research Council of Norway’s program FRIBIOØKO (project: “Life history strategies in ungulates: an experimental approach”). I have been employed by the Norwegian Institute for Nature Research, Arctic Ecology Department, Tromsø (NINA) and I have been a PhD-student at the Department of Biology, University of Tromsø (UiTø). I want to thank all persons who have contributed to the making of the thesis. Some persons have contributed significantly more than others and they, thus, deserve to be mentioned explicitly. First, I want to thank my two sets of supervisors: (i) Per Fauchald and Torkild Tveraa (unfortunately for them there is not a long distance between our offices); and (ii) Rolf A. Ims and Nigel G. Yoccoz (both at UiTø). Per and Torkild have spent countless hours on discussions, comments and other input that have been vital in forming the present thesis. Rolf and Nigel have also contributed significantly to the thesis through discussions of overall ideas and concepts, and they have given me prudent advices as well as constructive comments on several of the manuscripts. I want to thank Marius W. Næss, John-André Henden, Knut Langeland, Audun Stien, Øystein Varpe, Navinder J. Singh for their valuable contributions through discussions and comments on various manuscripts. I also want to thank all my colleagues at NINA for their support and for bringing so much fun into work. In that respect Jan O. Bustnes, Børge Moe, Kjell E. Erikstad, Sveinn A. Hanssen, Sidsel Grønvik, Gry H. Jensen, Jane A. Godiksen, Geir H. Systad and Sophie Bourgeon deserve special thanks for their encouragement and for sharing their wisdom about science and life in general. All my friends, especially Eirik M. Eilertsen, Sindre Dahlkvist, David Ingebrigsten, Marius W. N, John-André H., Knut L., Vegar Bjørkeng, Ståle Liljedal, Morten Jørgensen, Øystein V., Tarjei Tollefsen, Børge W. Larsen, Rune Nilsen, and Ole L. Hansen, have been a great source of motivation. I thank my son, Sigur Bårdsen, for bringing joy and meaning into my life, and Kristin L. Hansen and her family for their kind support. I also thank Kristin for doing more than her share in taking care of Sigur during both suddenly occurring fieldwork and during the process of finalizing this thesis. My family have supported me in this as in other parts of my life. In that respect warm thanks goes to my parents; Bjørg B. Bell and Uno Elvebakk, my brothers and sister; Johan E. Skalegård, Dag-Frode Bårdsen, Nils E. Skalegård and Britt-Mari Bell, my stepparents; Mikal O. Bell and Magdalena Skalegård, my nephews; Amalie S. Olsen, Oskar E. Skalegård and Ares E. L. Bårdsen, my ‘extra set of parents’ in Øverbygd; Joar and Janne Dahlkvist, as well as; Geir, Tone and Solveig Elvebakk, and Magnhild Ø. Bårdsen.

RISK SENSITIVE REPRODUCTIVE STRATEGIES 1

INTRODUCTION Biologists, anthropologists and psychologists have for a long time recognized that the theory of economic allocation of a limited budget can be useful in studies of optimal behaviour (e.g. Real and Caraco 1986, Stephens and Krebs 1986 ch. 6, Mace and Houston 1989, Mace 1990, 1993, Winterhalder et al. 1999). Risk sensitivity and related concepts have its roots within economical theory, but in biology risk sensitivity has its basis in studies of optimal foraging. The definition of risk used both in this thesis and its associated articles is similar to the definition used in risk sensitive foraging (reviewed in e.g. Real and Caraco 1986, Kacelnik and Bateson 1996): risk is defined as unpredictable variation in the outcome of behaviour, with consequences for an organism's fitness (the ultimate currency in evolutionary biology), utility (an economic currency) or value1 (a synonym for both currencies: sensu Winterhalder et al. 1999, Winterhalder 2007). It is important to keep in mind that the probability distribution of outcomes can be known to the organism based on past experience, but stochasticity makes it impossible for organisms to predict with certainty any particular future outcome (Kacelnik and Bateson 1996). Risk is not the same as uncertainty, i.e. incomplete information, as risk cannot be overcome simply by acquiring more information (Kacelnik and Bateson 1996, Winterhalder et al. 1999, Winterhalder 2007). Risk sensitivity analysis is relevant for a wide range of different behaviours, such as reproductive behaviour (e.g. Bednekoff 1996, Winterhalder and Leslie 2002), as risk sensitivity should be presumed important whenever: (i) the fitness function is nonlinear, and (ii) one or more of the behavioural alternatives is characterized by unpredictable fitness outcomes (e.g. Stephens and Krebs 1986, Kacelnik and Bateson 1996, Winterhalder et al. 1999, Winterhalder 2007). The fitness function (deduced from utility theory) makes an explicit assumption that organisms make consistent and rational choices based on the information they have at hand (Stephens and Krebs 1986). Specifically, organisms facing stochastic environments should solve two distinct problems: (i) the organisms must learn the fitness associated with different behaviours (‘a problem of information’); (ii) then, the organism must select a strategy for exploiting those distributions (‘a problem of risk’) (Real and Caraco 1986). First, individuals that successfully track environmental fluctuations will have a selective advantage over poor trackers (Boyce and Daley 1980). Second, the relationship between reward2 and fitness must be nonlinear if organisms are said to be risk sensitive (linear relationships imply risk neutrality: e.g. Stephens and Krebs 1986, Kuznar 2001, Kuznar 2002, Kuznar and Frederick 2003). If the fitness function is: (i) concave-down, i.e. negatively accelerating, individuals are said to be risk averse as the rate of increase in fitness decreases as the amount of reward increases (‘the law of marginal diminishing returns’); and (ii) concave-up, i.e. positively accelerating, individuals are said to be risk prone as each unit of additions reward is valued more than the previous (Stephens and Krebs 1986: Fig. 6.1-2). Risk sensitivity can, thus, be used to understand under what circumstances individuals are willing to

1 ‘Fitness’ is used instead of ‘utility’ or ‘value’ through the rest of this study. Utility measures ‘the level of satisfaction’

associated with a specific good or decision (Kuznar 2001) and this is the basic organizing principle that individuals subject to certain constraints seek to maximize (e.g. Real and Caraco 1986). This can be illustrated using an example from economy: winning a price of 100 € makes a substantial contribution to the utility of a poor person, whereas the same prize makes an insignificant contribution to the utility of a multi-millionaire.

2 ‘Reward’ can be used synonymously to ‘wealth’ or ‘good’, which is typically the same as ‘individual state’ (e.g. Houston and McNamara 1999).


accept or avoid gambling: being risk neutral3 means that the cost of loosing is similar to the benefit of winning; being risk averse3 means that the cost of loosing is large compared to the benefit of winning; whereas being risk prone3 means the potential cost is minor relative to the benefit. A central issue in life-history theory is how individuals allocate resources between current reproduction and future survival, a trade-off known as the cost of reproduction (e.g. Roff 1992, Stearns 1992). How environmental stochasticity affects life-history evolution is poorly understood except that long-lived organisms generally favor own survival over reproduction (e.g. Lindén and Møller 1989, Erikstad et al. 1998, Gaillard et al. 1998, Gaillard et al. 2000, Ellison 2003, Gaillard and Yoccoz 2003). Many organisms inhabit fluctuating environments, where fluctuations usually consist of a predictable seasonal component and a more unpredictable stochastic variation around this seasonal trend (Paper 4). Organisms inhabiting this type of environments have to make behavioural decisions without full knowledge about future environmental conditions (e.g. McNamara et al. 1995). Reproduction typically takes place during the favourable season (summer), whereas survival is particularly constrained in the unfavourable season (winter: Sæther 1997). In this type of environments, late winter conditions can have profound effects on both survival and reproduction (Coulson et al. 2000, Patterson and Messier 2000, Coulson et al. 2001, DelGiudice et al. 2002). Autumn body mass, which represents an insurance against winter starvation, is then traded against the resources a female can allocate to her offspring during summer as accumulation of fat reserves during summer might compete with lactation (Clutton-Brock et al. 1989, Clutton-Brock et al. 1996, Fauchald et al. 2004, Festa-Bianchet and Jorgenson 1998, Reimers 1972, Skogland 1985, Tveraa et al. 2003, Paper 1-2). Body mass is a proxy for condition or reserves, and an important trait affecting both survival and reproduction4. Consequently, in a given summer a female has to choose how many resources to allocate to somatic growth vs. reproduction: if a female allocates too much in reproduction this will reduce her ability to build an insurance against winter starvation (Paper 1-4). Risk sensitivity in the context of the present thesis can be understood as a combination of the probability of encountering an extreme winter and the consequences such winters have on fitness (Paper 1-4). First, the outcome of a given reproductive allocation on survival is unpredictable due to the stochastic nature of winter climatic conditions (Paper 4): even though females might have ‘estimated’ this statistical distribution based on previous experience, environmental stochasticity makes any reliable forecasting of climatic events practically impossible5. Second, the relationship between winter weather conditions and fitness is nonlinear as: (i) the combination of an extremely harsh winter and low body reserves is not only fatal for reproductive success (e.g. juvenile and

3 In the ‘standard design of risk sensitive foraging experiments’ (reviewed by Stephens and Krebs 1986, Kacelnik and

Bateson 1996) risk prone and risk averse have been defined as: “Given a choice between two equal means, an organism is said to be risk-prone if it prefers the more variable option and risk-averse if it prefers the less variable option” (Houston 1991). Conversely, an individual is risk neutral if it shows no preference.

4 Body mass acts as a state variable (e.g. Houston and McNamara 1999), which is a currency that can be traded for reproduction or survival.

5 Since meteorologists do only produce reliable predictions of weather phenomena for more than perhaps a few days into the future it is unlikely that wild herbivores can predict weather ~7 month into the future. Meteorologists have an advanced knowledge about weather systems (high level of information), but the stochastic nature of these systems makes accurate predictions far into the future impossible. The Norwegian Meteorological Institute, for example, does not forecast more than three months into the future (http://retro.met.no/sesongvarsler/introduksjon.html).

http://retro.met.no/sesongvarsler/introduksjon.html


neonatal survival) but it can even greatly reduce adult survival (Skogland 1985, Clutton-Brock et al. 1992, Clutton-Brock et al. 1996, Aanes et al. 2000, Aanes et al. 2002, Tveraa et al. 2003); whereas (ii) extremely benign winters do not represent bonanzas as survival and reproduction are not boosted way above that of an average winter (Fauchald et al. 2004, Paper 1-3). Using terms from risk sensitivity, such an asymmetric response in the costs and benefits relative to environmental unpredictability indicates that long-lived organisms should be risk averse as they should be unwilling to expect the coming winter to be a benign one (Paper 1). It is important to keep in mind that organisms cannot manipulate the probability of encountering a harsh winter, but they can buffer the adverse consequences of such winters by reducing their summer reproductive allocation in order to increase their own autumn body reserves (Adams 2005, Paper 1). Organisms inhabiting such systems should not prepare for an average winter, but for extreme events that might happen from time to time (Paper 2). The optimal reproductive strategy will, thus, depend on the expected winter environmental conditions. A changed distribution in winter conditions can have important consequences for both reproduction and survival. Individuals experiencing stable and benign winter conditions can afford a low autumn body mass and might therefore increase their reproductive allocation. On the other hand, animals experiencing harsh and variable winter conditions should maximize their autumn body mass by lowering their reproductive allocation. Accordingly, organisms experiencing unpredictable environments should adopt a risk sensitive reproductive strategy by adjusting their reproductive allocation during summer according to the chance of starvation the following winter (Paper 1-4). For a given body mass and distribution of environmental conditions, individuals can play different strategies (Paper 4). A risk prone reproductive strategy involves high reproductive allocation that will result in high reproductive reward during benign conditions, but high survival cost during harsh conditions. A low reproductive allocation will, on the other hand, result in high winter survival, but a low reproductive reward and represents a risk averse reproductive strategy. Moreover, when benign conditions appear for many years, individuals should increase their reproductive allocation as the amount of autumn body reserves that is needed for insurance against winter starvation will be lowered under such conditions. Population density, which in interaction with winter climate, can have profound negative effects on survival and reproduction (e.g. Grenfell et al. 1998, Coulson et al. 2000), are confounded with environmental conditions as harsh conditions generally supports lower densities than benign conditions (e.g. Morris and Doak 2002). Thus, density may also affect the optimal reproductive allocation strategy (Paper 3-4). For example, increased densities of reindeer Rangifer tarandus have direct effects on the individuals through increased competition for resources (Tveraa et al. 2007), and indirect effects through long-term effects on the pastures (Bråthen et al. 2007, Tveraa et al., unpublished results). In sum, environmental conditions and density have effects on how organisms should allocate resources between reproduction and somatic growth (Paper 1-4). A risk sensitive reproductive strategy is one of several factors that can be of importance for population dynamics (Paper 4). Populations of large terrestrial mammalian herbivores (with an adult mass ≥ 10 kg: Gaillard et al. 2000 hereafter referred to as ‘large herbivores’) in northern and seasonal environments show different population dynamics. How individuals allocate resources into reproduction may provide an explanation for this. The Soay sheep Ovis aries on Hirta, Scotland


has, for example, a high population growth rate due to a high fecundity, low age at first reproduction and early lambing (Clutton-Brock et al. 1996, Clutton-Brock and Coulson 2002, Clutton-Brock and Pemberton 2004). Over-compensatory density dependence combined with harsh environmental conditions results in more or less regular events of mass starvation and population crashes during winter (Clutton-Brock et al. 1996, Grenfell et al. 1998, Coulson et al. 2001). In contrast, red deer Cervus elaphus on Isle of May, Scotland has a much lower population growth rate (Clutton-Brock et al. 1987). The population is regulated through a low fecundity, late age at maturity, late calving and direct density dependent juvenile mortality resulting in relatively stable populations (Clutton-Brock and Coulson 2002). In semi-domestic reindeer, Norway differences in productivity, due to differences in reproductive allocation as an adaptation to buffer winter climate severity (Paper 1-3), can have profound effects on population dynamics as: a combination of climate severity, harvest and foraging conditions has a profound impact on average population densities, individual body masses, and population dynamics (Tveraa et al. 2007). In sum, differences in reproductive strategies might have important consequences on the cost of reproduction and on population dynamics (Clutton-Brock et al. 1996, Clutton-Brock and Coulson 2002, Paper 4). Apart from the assumptions underlying risk sensitivity, a few more assumptions should be fulfilled for defining risk sensitive reproductive strategies. First, organisms must be fitness maximizing, which is not an assumption specific for this study as it is a general assumption for evolutionary biology as a discipline (e.g. McNamara 2000, Coulson et al. 2006). Second, the organism of interest should be iteroparous (i.e. long-lived with many potential breeding attempts per lifetime: Schaffer 1974, Stearns 1992). This assures that an organism can spread the cost of breeding across several attempts. Third, the organism should experience unpredictable costs of reproduction. If no cost of reproduction does occur or if this cost is predictable there is no reason for spreading the potential negative consequences of reproduction over several breeding attempts. Fourth, the organism should be able to build energy reserves functioning as insurance against adverse environmental conditions. Fifth, the environment inhabited by the organism should be characterized by either strong seasonality (a favourable breeding season and an unfavourable non-breeding season) or at least by periods of favourable and unfavourable conditions. During the favourable season, organisms trade resources to reproduction against resources for building body reserves. The overall objective of this thesis was to investigate how environmental conditions affect reproductive strategies, and to investigate how interactions between optimal reproductive strategies and the environment can shape population dynamics. This thesis uses reindeer as a biological model as this species fulfils the above assumptions. The following research questions were addressed:

(1) How do improved and reduced winter feeding conditions on a short-term basis affect how individuals allocate their resources between reproduction and gain in body mass during summer (Paper 1-3)?

(2) How do long-term changed winter feeding conditions affect summer reproductive allocation (Paper 1-2)?

(3) How does the cost of reproduction vary according to individual quality, and factors extrinsic to the individuals like winter climatic conditions and population density (Paper 1-4)?

(4) How do winter climatic conditions affect the optimal reproductive strategy (Paper 4)? (5) How do plastic life histories and climate affect population dynamics (Paper 4)?


METHODS Study species and area

Reindeer belongs to the family Cervidae and the order Cetartiodactyla (Price et al. 2005). Cetartiodactyla is a relatively new order that includes the two former orders: Artiodactyla (‘even-toed hoofed mammals’) and Cetacea (whales & dolphins) (Price et al. 2005). Reindeer is a sexually dimorphic species where females are smaller than males (e.g. Reimers 1983, Reimers et al. 1983), and during most of the year the sexes are separated. The rut and conception happens in the autumn (e.g. Skogland 1994), and calving usually takes place in May (Reimers et al. 1983, Flydal and Reimers 2002). Reindeer are group living and highly migratory as they move between distinct summer and winter pastures (e.g. Folstad et al. 1991, Skogland 1994, Fauchald et al. 2007). The thesis is based on empirical data from two semi-domesticated herds in Northern Norway (Paper 1 & Paper 3) and one in Northern Finland (Paper 2). The number of semi-domestic reindeer in Norway increased towards the late 1980’s (e.g. Paper 3:Fig. 1a). This trend was particularly strong in the northernmost part of Norway, where the peak in reindeer numbers was followed by a population decrease that continued throughout the 1990’s (Tveraa et al. 2007: Fig. 1). The herds are organized in herding districts that are separated by fences and natural boarders. Since all animals are ear marked according to owner, virtually no effective movement between different populations exist (Tveraa et al. 2007). Our data source in Finland is from the research herd in Kaamanen, which consist of ~80 females with known life histories (Paper 2). Scientific approach

Research on large herbivores has generally been performed using descriptive long-term observational studies and lack of experimental manipulations (Caughley 1981, Gaillard et al. 1998). Experiments on wild animals can be difficult to perform for practical reasons, especially for long-lived species that covers large geographical area, as experiments can be time consuming, expensive and impracticable (Turchin 1995). Consequently, there is still a need for long-term studies of marked individuals and with experimental designs that allow the relationship between population parameters and variables such as climate and density to be estimated (Festa-Bianchet et al. 1998, Gaillard et al. 1998). Semi-domestic reindeer provides a unique opportunity in this context because: (i) herds are gathered at least once each year for marking and slaughtering (e.g. Paper 1 & Paper 3); (ii) they are managed within and exposed to the same natural environment as wild reindeer used a long time ago (Parks et al. 2002); (iii) it is easier to identify the mechanisms causing demographic changes in larger compared to smaller organisms (Sæther 1997); and (iv) it is possible, within a reasonable time frame, to generate knowledge of importance to researchers, authorities, as well as reindeer herders. Ecological questions should be assessed with an analytical approach that combines statistical analyses of observational data, experiments, and mathematical models (Turchin 1995). The present thesis tests a common scientific hypothesis using these three approaches: an experimental protocol (Paper 1 & Paper 2); an observational protocol (Paper 3); and a theoretical model (Paper 4). The


three approaches have different advantages and disadvantages. First, well-designed experiments6 have an advantage compared to the other approaches as this type of studies can make so-called ‘design-based inference’, which is called ‘strong inference’ due to its ability to reveal evidence of causation (e.g. Quinn and Keogh 2002, Crawley 2003, Yoccoz and Ims 2008). A critical issue in ecological experiments, however, is whether the applied treatment is relevant for addressing the research question of interest and if the level of treatment is realistic with respect to a natural setting (discussed in Paper 1 & Paper 2). Second, observational studies, which do not include the design properties of experiments, have the advantages of assessing research questions in a natural setting. This advantage, however, comes with the cost of possible confounding (discussed in Paper 3:S1). As observational protocols can only reveal ‘model-based inference’ they are often said to reveal ‘weak inference’ (e.g. Quinn and Keogh 2002, Crawley 2003, Yoccoz and Ims 2008). Third, models are useful tools in assessing mechanisms that might occur in nature. Numerous definitions exists of what models are and what they can be used for, but as there exist many different types of models developed for a wide range of different topics I will not enter such a general discussion. In the context of the present thesis it might, however, be useful to think of a model as an idealized, or simplified, representation of reality. These sorts of ‘conceptual models’ can be viewed as tools for testing arguments in a formal mathematical setting, where models can be used to test if specific patterns emerge from known processes and mechanisms given a set of more or less realistic assumptions (e.g. Kokko 2007). Study design

Manipulation of winter conditions: supplementary feeding vs. natural pastures (Paper 1) In both experiments in this study, which was performed in Northern Norway, females were included and allocated to different experimental groups according to the order in which they appeared in the corral. This was done under the assumption that this represented a sufficient randomization. We tested the design with respect to initial female body mass, a potentially confounding covariate (see Introduction), and as this state variable was equally distributed within the experimental groups we concluded that the study was sufficiently randomized. We used one herd where females had received supplementary feeding for years, and another herd where females utilized only natural pastures (see Paper 1:Fig. 1 for details). Manipulation of winter feeding conditions on a short-term basis was performed by moving individuals from one herd to the other: (i) translocation of individuals from the herd utilizing natural pastures to the herd receiving supplementary feeding (‘improved winter conditions’); and (ii) translocation of individuals from the herd receiving supplementary feeding to the herd utilizing natural pastures (‘reduced winter conditions’). Additionally, the control groups from the two experiments were used in an analysis of the effects of long-term supplementary feeding. Individual body mass as a response was recorded during summer, autumn and the coming winter. Multiple observations of females with a calf at foot were used to identify mother-calf relationships or whether a female was barren within a given year. The experiments were replicated in two different years (2003 & 2004) using a new set of individuals, and individuals were followed from January (initiation) to the next January (finalization).

6 The following assumptions are often discussed: manipulation (including controls), randomization, replication, realism

and representation.


Manipulation of winter conditions and reproduction: supplementary feeding and reproduction (Paper 2) This experiment was performed in Northern Finland during 2007-2008. Only initially pregnant females were included in this experiment, and a stratified-randomized design ensured that initial female body mass, and consequently also initial age, had the same distribution in the experimental groups (Paper 2). Individuals were assigned to one of two experimental manipulations: (i) environmental manipulation, which consisted of control females on natural pastures and a group of females receiving supplementary feeding; and (ii) reproductive manipulation, which consisted of control females that were lactating and a group where the offspring was removed 0-2 days after parturition (see Paper 2:Fig. 1 for details). Individual body mass, as a response, was recorded during winter, spring, summer, autumn, and the coming spring. Newborns were caught by hand and individually marked, and body mass, date of birth as well as offspring sex were also recorded. Individuals were followed from January (initiation) to April next year (finalization). Increased population abundance and varying winter conditions: following two herds for six years (Paper 3) This observational study was initiated by the marking of fifty prime-aged females (≥1 year) in each of two herds in Northern Norway. Both herds utilize the same winter pastures where they are kept together through the winter, but utilize different summer pastures. None of the herds were given supplementary feeding. The herds are separated on the winter pastures in the spring, and they are then herded to their respective summer pastures at the coast (Paper 3:Fig. 2). During the autumn migration, on the way back to the winter pastures, the two herds are again mixed and the annual migration cycle is ended. Individual body mass was recorded during spring and autumn, whereas calf production, mother-calf relationships and whether a female was barren or not were assessed similar as in the first study (Paper 1). Individuals were followed from April 2002 (initiation) to April 2008 (finalization). During this period population size increased dramatically. Manipulating winter climate: changing the distribution of winter environmental conditions (Paper 4) This simulation model, which is a follow-up to the previous empirical studies (e.g. Paper 1-3), used a state-dependent individual-based model (IBM) to investigate how females should optimize their reproductive investment in a stochastic environment that contains density dependent processes. The model excludes males as the aim was to assess female life-histories and because important parameters were widely available for females but not for males. Each time step was discrete (equalling one year) and divided in two distinct seasons: (i) summer where density dependent competition among individuals over a shared food resource occurred; and (ii) winter where temporal variability in environmental conditions affected individual survival and body mass losses. Individuals did not know the state of the coming winter conditions at the time when reproduction took place (summer). Winter environmental conditions were simulated assuming a normal distribution with three different average winter conditions (‘control’, ‘improved’ and ‘reduced’) and a gradient the distribution’s standard deviation to mimic a gradient in environmental unpredictability.


RESULTS Short-term changes in winter feeding conditions (Paper 1-2)

An asymmetric response to short-term improved vs. reduced winter conditions was present. When food availability was reduced, females immediately reduced their reproductive allocation the following summer (Paper 1 & Paper 2), presumably in order to not compromise their own body mass at the onset of the next winter. On the contrary, when winter conditions were improved females were reluctant to increase their reproductive allocation (Paper 1). A small positive effect of short-term improved winter conditions was, however, found on offspring birth mass of initially smaller females in one study (Paper 2). Long-term changed winter feeding conditions (Paper 1-3)

In contrast to short-term improved conditions, females that had been provided additional winter forage over several years allocated more in summer reproduction indicating that reindeer can track consistent changes in winter conditions (Paper 1). Moreover, winter feeding conditions for the Finnish herd, which has received supplementary feeding for years, were superior to most other Fennoscandian herds (Paper 2). This has probably resulted in an increased reproductive allocation by females in this herd as both reproductive success and offspring body masses were particularly high in this herd compared to the two other empirical studies (Paper 1 & Paper 3). Female body mass was, however, also on average higher in the Finnish herd compared to the two Norwegian herds. This could be used as evidence against an increased reproductive allocation, but this might also indicate that these females have reached an upper threshold for which additional body mass does not translate into larger offspring or increased reproductive success. This can be explained by the fact that female reindeer are normally constrained to producing only one offspring per year so the consequence of allocating too many resources into reproduction during gestation can at best lead to giving birth to one very obese offspring. The cost of reproduction and environmental conditions (Paper 1-4)

Winter conditions were unpredictable even though the degree of environmental stochasticity was varying across study areas (Paper 2 vs. Paper 1 & Paper 3); and extremely harsh and benign winters have asymmetric, or nonlinear, negative and positive consequences for the cost of reproduction (Paper 2 & Paper 4). Lactating females gained less body mass during summer compared to barren ones (Paper 2-3). Additionally, this difference was negatively related to population density and winter climate indicating that a higher competition for resources had a more profound negative effect of reproducing compared to barren females (Paper 3). Moreover, successfully reproducing females allocated fewer resources into future reproduction by producing smaller offspring in the coming year (Paper 3). Individual quality was also of importance as: female body mass was a positive predictor of offspring body size within a period of ~9 months from birth (Paper 1-3); and successfully reproducing females experienced an enhanced probability of giving birth the next year (Paper 3). Environmental conditions and optimal reproductive strategies (Paper 4)

The model (Paper 4), which synthesizes our understanding of the empirical results, showed that winter climatic conditions had a large effect on the amount of resources that reindeer should


allocate to reproduction vs. somatic growth during summer. This study generally confirmed the finding in the empirical studies (Paper 1-3). This study, however, also went a bit further as it showed that plastic reproductive strategies were superior compared to fixed strategies in all types of environments (Paper 4). For adults following a plastic strategy, reproductive allocation was estimated and updated each year according to the individuals’ spring body mass. This ensured that females in poor body condition during spring either skipped reproduction or reduced their reproductive allocation in order to enhance their body reserves during summer. A fixed strategy, on the other hand, implied that females always allocated a constant proportion of its spring body mass to reproduction (Paper 4:A1). This severely limited females following this strategy from buffering periods of reduced forage availability. Plastic strategies with a low reproductive allocation per unit female spring body mass did win in the most unpredictable environments (Paper 4:Fig. 3). This relationship was, however, weakest for improved environmental average. Similarly, strategies involving a higher reproductive allocation per unit spring body mass did win in more predictable environments for all environmental averages except for the improved one. The latter was more an effect of population density, which was confounded with environmental conditions (Paper 4:Fig. 5). Moreover, the realized average reproductive allocation interacted with environmental average and stochasticity, and average population density: the lowest reproductive allocation was found in harsh and unpredictable winter conditions and during high density (Paper 4:Fig. 4). Environmental conditions, reproductive allocation and population dynamics (Paper 4)

Populations inhabiting benign and predictable winter conditions were most sensitive to climatic perturbation. These populations supported the highest population densities, which in interaction with climate limited the possibility for individuals to buffer adverse climatic effects. Negative density dependence had a strong negative effect on offspring body mass and consequently on reproductive success: the combination of high density, which resulted in lowered offspring autumn body mass, and an extremely harsh winter had dramatic negative effects on offspring survival. A high reproductive allocation also resulted in lowered female autumn body mass in these good environments, which gave the potential for very low adult survival rates in the rare occasions of an extremely harsh winter. Populations subject to poor winter conditions were, on the other hand, characterized by low density, and these populations were least sensitive to climate. A low reproductive allocation resulted in increased female autumn body mass, and a consequently high adult survival in these environments. This model did not include any predation or harvest, but harsh winters apparently ‘harvested’ these populations by removing especially younger individuals. This released these populations from negative density dependence, and this had a positive effect on reproduction as females received a higher reproductive reward (for a given allocation value) during low compared to high density (Paper 4:A1).


DISCUSSION Female reindeer, which are long-lived with many potential breeding attempts during a lifespan, do not want to jeopardize their own survival over reproduction. Consequently, females have adopted a risk sensitive reproductive strategy where they trade reproduction against the amount of autumn body reserves needed for survival insurance during the coming winter (Paper 1-4). Being risk sensitive implies that individuals to some degree are either risk prone or risk averse, where female reindeer are risk averse because: (i) during the summer they cannot predict with certainty the coming winter; and (ii) extremely harsh and benign winters have asymmetric fitness consequences (mainly through their effects on adult survival). Female reindeer are, thus, not willing to gamble that a coming winter will be a benign one, because the cost of preparing for a benign winter but meeting a harsh one is dramatically higher than the benefit of preparing for a benign winter and actually get one. Consequently, female reindeer optimized their allocation in reproduction vs. somatic growth according to expected winter conditions, but individuals do not prepare for an average winter, but for extreme winters (relative to past experience) that might happen from time to time. Such effects of environmental conditions on life histories have important consequences for both individual survival and reproduction, and hence also on population dynamics. Many of the assumptions for a risk sensitive reproductive investment are, at least partly, fulfilled for many long-lived organisms as they experience a temporally varying cost of reproduction, they build body reserves during periods of favourable environmental conditions and they use these reserves as a buffer against unpredictable environmental variability during periods of non-favourable conditions [e.g. humans (Bronson 1995, Lummaa and Clutton-Brock 2002), large herbivores (Sæther 1997, Gaillard and Yoccoz 2003), birds (Lindén and Møller 1989, Parker and Holm 1990, Hanssen et al. 2005), fish (van den Berghe 1992, Hutchings 1994, Klemetsen et al. 2003) and reptiles (Shine 2005, Radder 2006)]. The ability for individual’s to buffer negative climatic effects by adopting a risk averse reproductive strategy has important consequences for how the impacts of future climate change will be. These changes will most likely result in a shift towards more frequent extreme precipitation events (e.g. Wilby and Wigley 2002, Semmler and Jacob 2004, Tebaldi et al. 2006, Benestad 2007, Sun et al. 2007). Moreover, many of these climatic scenarios are expected to happen both sooner and more pronounced in the northern hemisphere (e.g. Tebaldi et al. 2006, Benestad 2007), which is why current efforts to understand the impacts of future climate change should focus on these systems. Hanssen-Bauer et al. (2005), for example, review several studies predicting how future climate change will affect Fennoscandia. The most important finding of this, and other studies, is a predicted shift between warm and cold periods during winter coupled with a year-round increased intensity of precipitation. Such shifts will lead to an increased frequency of wet weather, deep snow and ice crust formation that has negative consequences for large herbivores (e.g. Solberg et al. 2001). Many recent analyses of climatic effect signatures in population time series have been used to infer the likely consequences of future climate change (Stenseth et al. 2002). The impact of future climate change commonly invokes more frequent population collapses (e.g. Post 2005). Such


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PAPER 1

Experimental evidence for a risk sensitive

life history allocation in a long-

lived mammal

Bårdsen, B.-J., P. Fauchald, T. Tveraa, K. Langeland, N. G. Yoccoz

& R. A. Ims

Ecology 89:829-837

Ecology, 89(3), 2008, pp. 829–837� 2008 by the Ecological Society of America

EXPERIMENTAL EVIDENCE OF A RISK-SENSITIVE REPRODUCTIVEALLOCATION IN A LONG-LIVED MAMMAL

BARD-JØRGEN BARDSEN,1,2,3 PER FAUCHALD,1,2 TORKILD TVERAA,1 KNUT LANGELAND,1,2

NIGEL GILLES YOCCOZ,1,2 AND ROLF ANKER IMS1,2

1Norwegian Institute for Nature Research (NINA), Division of Arctic Ecology, Polar Environmental Centre, N-9296 Tromsø, Norway2University of Tromsø (UIT), Department of Biology, N-9037 Tromsø, Norway

Abstract. When reproduction competes with the amount of resources available forsurvival during an unpredictable nonbreeding season, individuals should adopt a risk-sensitiveregulation of their reproductive allocation. We tested this hypothesis on female reindeer(Rangifer tarandus), which face a trade-off between reproduction and acquisition of bodyreserves during spring and summer, with autumn body mass functioning as insurance againststochastic winter climatic severity. The study was conducted in a population consisting of twoherds: one that received supplementary winter feeding for four years while the other utilizednatural pastures. The females receiving additional forage allocated more to their calves.Experimental translocation of females between the herds was conducted to simulate twocontrasting rapid alterations of winter conditions. When females receiving supplementaryfeeding were moved to natural pastures, they promptly reduced their reproductive allocationthe following summer. However, when winter conditions were improved, females werereluctant to increase their reproductive allocation. This asymmetric response to improved vs.reduced winter conditions is consistent with a risk-averse adjustment in reproductiveallocation. The ability of individuals to track their environment and the concordant risk-sensitive adjustment of reproductive allocation may render subarctic reindeer more resilient toclimate change than previously supposed.

Key words: cost of reproduction; environmental stochasticity; life history; phenotypic plasticity; prudentparent; Rangifer tarandus; reindeer.

INTRODUCTION

A central issue in life history theory is how individuals

allocate resources between current reproduction and

future survival (e.g., Roff 1992, Stearns 1992). In large

mammals and birds, these demographic parameters are

highly correlated with body mass (e.g., Sæther 1997,

Lummaa and Clutton-Brock 2002). In reindeer (Rangi-

fer tarandus), for example, both survival and successful

reproduction are positively related to size; larger females

are more likely to reproduce and produce larger calves

than are small females (Kojola 1993, 1997, Tveraa et al.

2003).

In mammalian herbivores with long life spans,

individuals favor their own survival over reproduction.

Hence, reproductive output and juvenile survival are

more variable than adult survival (Gaillard et al. 1998,

2000, Gaillard and Yoccoz 2003). However, the balance

between reproduction and survival should depend on

environmental conditions affecting the two traits (see,

e.g., Sæther 1997, Forchhammer et al. 2001, Gaillard

and Yoccoz 2003). This trade-off is especially important

in northern temperate environments where reproduction

takes place during the favorable season, whereas

survival is particularly constrained in the unfavorable

season (Sæther 1997). If, for example, winter conditions

are improved, fewer resources are needed for survival

and more resources should be allocated to reproduction.

In a variable environment where the resources needed

for survival during winter are difficult to predict, long-

lived species should adopt a conservative reproductive

strategy in which individuals should retain sufficient

body reserves to ensure survival during especially harsh

winters (see Erikstad et al. 1998). In the present study,

we translocated reindeer between two herds experiencing

different winter but similar summer conditions. Specif-

ically, we experimentally improved and reduced winter

conditions for the two herds.

For large herbivores in northern and clearly seasonal

environments, late-winter conditions have profound

effects on survival and reproduction (e.g., Coulson et

al. 2000, 2001, Patterson and Messier 2000, DelGiudice

et al. 2002). Accordingly, Tveraa et al. (2003) found that

harsh winter conditions greatly reduced adult survival

and fecundity in reindeer the following summer. To

disentangle the impact of late-winter and spring

conditions in reindeer, Fauchald et al. (2004) performed

an experiment in which feeding conditions were im-

proved during late winter and the calving season.

Reindeer given additional winter forage greatly in-

Manuscript received 13 March 2007; revised 21 May 2007;accepted 1 June 2007; final version received 11 July 2007.Corresponding Editor: T. J. Valone.

3 E-mail: [email protected]

829

creased their body mass in the late winter relative to

early-winter body mass. However, during the calving

season, females given additional winter forage rapidly

lost their additional body mass. After calving, there were

no effects of winter feeding on either body mass or

survival of females and calves. Consequently, Fauchald

et al. (2004) suggested that female reindeer regulate their

body mass down to some minimum threshold during

spring, when the risk of starvation is low, in order to

take care of their newborn calves. Hence, additional

winter body mass acts primarily as an insurance against

periods of winter starvation. However, autumn body

mass, and hence the insurance against winter starvation,

is traded against the resources that a female allocates to

her calf during summer (Reimers 1972, Skogland 1985,

Clutton-Brock et al. 1996, Tveraa et al. 2003, Fauchald

et al. 2004). This trade-off implies that prevailing winter

conditions, in terms of severity and predictability, might

have profound effects on reproductive allocation for

northern large herbivores (Tveraa et al. 2007). Animals

experiencing stable and benign winter conditions can

afford a low autumn body mass and might therefore

increase their fecundity and reproductive allocation. On

the other hand, animals experiencing harsh and variable

winter conditions should maximize their autumn body

mass and should therefore be limited by a relatively low

fecundity and reproductive allocation. Accordingly,

northern large herbivores might have adopted a risk-

sensitive reproductive strategy in the sense that they

adjust their reproductive allocation during summer

according to the risk of starvation in the following

winter (see Stephens and Krebs [1986] and Kacelnik and

Bateson [1996] for a discussion of the concept of risk

sensitivity). Risk sensitivity rests on the assumption that

individuals are capable of tracking environmental

variability (Stephens and Krebs 1986). Individuals that

successfully track environmental fluctuations, e.g., by

limiting their reproductive effort and increasing somatic

growth when resource availability is low, will possess a

selective advantage over poor trackers (Boyce and Daley

1980).

Experimental manipulations of reproduction in free-

ranging large mammals are difficult (e.g., Festa-Bianchet

et al. 1998). Here, we set up two experiments in subarctic

Norway designed to test predictions about risk-sensitive

reproductive allocation in reindeer. Semidomestic rein-

deer in Fennoscandia offer a unique opportunity to

experiment on a wide-ranging large herbivore (e.g.,

Tveraa et al. 2003, Fauchald et al. 2004, Holand et al.

2007, Røed et al. 2007). Most herds are kept free-

ranging on the same natural pastures in which wild

reindeer roamed about three centuries ago (e.g., Parks et

al. 2002). In modern times the reindeer husbandry has

adopted alternative herding strategies, including addi-

tional winter feeding on natural pastures (e.g., Parks et

al. 2002). We utilized this setting by studying two herds

within one interbreeding population. The ecology of the

two herds differed only in that one of the herds had

received additional winter forage since 2000, whereas the

other herd had access solely to natural pastures. InJanuary 2003, we translocated females between the two

herds, resulting in two experiments in which one herdfaced reduced winter conditions while the other faced

improved winter conditions. The experiments wererepeated in 2004.

For a given distribution of winter conditions, a ‘‘risk-prone’’ reproductive strategy involves high reproductiveallocation that will result in high reproductive reward

during benign winters, but high survival cost duringharsh winters. A low reproductive allocation will, on the

other hand, result in stable winter survival, but lowerpotential reproductive reward. Consequently, this rep-

resents a ‘‘risk-averse’’ reproductive strategy. Becausesubarctic reindeer are long-lived, large mammals living

in a strongly seasonal environment with severe wintersthat can even compromise the survival of adults (Tveraa

et al. 2003), we expected them to be on the risk-averseside of the risk-prone–risk-averse continuum. However,

when benign winter conditions appear over severalyears, even risk-averse animals should increase their

reproductive allocation during summer if they are ableto perceive the improved predictability of their environ-

ment (Gaillard and Yoccoz 2003). Accordingly, weinvestigated whether there was an increase in reproduc-tive allocation due to a long-term feeding manipulation.

On the other hand, improved winter conditions over justone season, according to a risk-averse reproductive

allocation, should not provide a sufficiently strong cueto induce an altered reproductive allocation. We thus

predicted that there would be no pronounced change inreproductive allocation in the short-term translocation

experiment where winter conditions were improved.However, according to a risk-averse reproductive

allocation, reindeer should be sensitive to a reductionin winter conditions. Thus, we expected an immediate

response to experimentally reduced winter conditions inthe sense that females should favor gain in own body

mass over calf production.

METHODS

Study population and long-term feeding manipulation

The present study was conducted in East Finnmark[698150–708030 N; 248300–248580 E], Northern Norway.

The study population, which includes more than the twoherds in the present study, is free-ranging most of the

time, utilizing a summer pasture area of ;400 km2.Since the harsh winter of 2000 (Tveraa et al. 2003), one

herd was kept in a separate subarea from Febru-ary/March until post-calving in late May, during which

period the reindeer were given commercial reindeerpellets at ;800 g�individual�1�d�1 (Poron-Herkku,

Raisio, Finland). Additional forage was provided usingseveral feeding dispensers to ensure that subordinateindividuals also had access to food. The other herd was

free-ranging on natural pastures in all seasons. Fromlate May the two herds were mixed, and they utilized the

BARD-JØRGEN BARDSEN ET AL.830 Ecology, Vol. 89, No. 3

same pastures until they were separated again in the

following January.

Protocol of the translocation experiments

On 11 January 2003 and 3 January 2004, animals

from the two herds were gathered. Each year a

subsample of 40 females (.1.5 years old) from each

herd was assigned to either of two experimental groups:

(1) a control kept in the original herd and (2) a treatment

moved to the other herd (Fig. 1). The females were

selected in the order in which they appeared in the

corral. Thus, the subsample of females does not

represent a random sample from the entire herd, but

each individual from the subsample was randomly

allocated to one of the different experimental groups.

The females and their calves were then followed until the

next January. Individual body mass and presence

(‘‘present’’ or ‘‘absent’’) was recorded on gatherings on

2 and 4 July, on 19 and 18 September, and on 11 and 3

January in 2003 and 2004, respectively. Individual body

mass was recorded to the nearest 0.2 kg using an

electronic balance (Avery Berke1, Birmingham, UK).

Multiple observations of females with a calf at foot were

used to identify mother–calf relationships or whether a

female was barren. We updated positive calf sightings

backward; a calf not observed in September but present

in January (as we recorded its body mass) was assumed

present in September. Consequently, we used updated

calf presence in September as a proxy for production

because the herd gathering in January only provided us

information about calf presence based on recorded body

masses.

Based on this design, we did the following compar-

isons (Fig. 1): (1) control (natural pastures) vs. control

(supplementary feeding) to quantify possible effects of

long-term improved winter conditions (hereafter termed

‘‘long-term feeding manipulation’’); (2) control (natural

pastures) vs. improved winter conditions (experimental

translocation to the herd receiving supplementary

feeding) to quantify possible effects of short-term

improved winter conditions (Experiment I: hereafter

termed ‘‘improved winter conditions’’); (3) control

(supplementary feeding) vs. reduced conditions (exper-

imental translocation to the herd utilizing natural

pastures only) to quantify possible effects of short-term

reduced conditions (Experiment II: hereafter termed

‘‘reduced winter conditions’’).

Statistical analyses

Missing values and initial female body mass.—There

were some missing values of body mass due to

individuals that eluded body mass recording or were

missing during gathering. The effect of missing values on

initial female body mass, a potentially confounding

covariate (e.g., Kojola 1993, Clutton-Brock et al. 1996,

Festa-Bianchet et al. 1998, Kojola et al. 1998, Tveraa et

al. 2003, Adams 2005) controlled for in the experimental

design, was examined in a two-way ANOVA with year

included as an additional factor. In total, six and 13

individuals were missing at least once in the ‘‘improved

winter conditions’’ during 2003 and 2004, respectively,

FIG. 1. The study was designed with respect to initial body mass (measured at the initiation of the experiments), which was usedto assign 20 females (/) to the control (C) and treatment (T) group, used as contrasts in Experiment I (improved; CI vs. TI) andExperiment II (reduced; CII vs. TII), respectively (Tables 2b, c and 3a, b). Manipulation of winter feeding conditions was performedin late winter by moving individuals from one herd to the other (the herds are represented by the parallel horizontal lines of boxes).The experiments were replicated in two different years, i.e., a new set of individuals was followed from January (initiation) to thenext January (finalization). The two experiments represent not only two different sets of current winter conditions, but alsodifferent prevailing winter conditions, as supplementary feeding has been carried out for several years in one of the herds.Consequently, the control groups from the two experiments were used in an analysis of the effects of long-term feedingmanipulation (CII contrasted on CI; Tables 1 and 2a).

March 2008 831RISK-SENSITIVE REPRODUCTIVE ALLOCATION

whereas this number was seven and 13 in the ‘‘reduced

winter conditions.’’ There was no evidence for differ-

ences in mean initial body mass between the two groups

of animals: individuals present at all times vs. individ-

uals absent at least once. The difference between the

groups was �0.37 kg (95% confidence limits [�3.05,2.32], dfmodel ¼ 3, 77) in the ‘‘improved winter

conditions’’ and �0.05 kg ([�2.75, 2.65], dfmodel ¼ 3,

77) in the ‘‘reduced winter conditions’’ after controlling

for the effect of year. All statistical analyses were carried

out in R (R Development Core Team 2006).

Body mass and reproductive success.—Linear mixed-

effect models (LME) applied using the NLME package

(Pinheiro and Bates 2000, Pinheiro et al. 2006) were used

to analyze the effect of the predictors on body mass of

the females and their calves. Experimental manipulation

(control and treatment; reduced and improved winter

conditions in each experiment, respectively), year (2003

and 2004), initial female body mass (January prior to

manipulation), and season (July, September, and Janu-

ary) were applied as fixed effects (Fig. 1), whereas

individual was included as a random effect (Pinheiro and

Bates 2000). All mixed-effect models in the present study

were fitted with random intercepts only. In order to

assess whether reindeer have adopted a risk-sensitive

reproductive allocation, it is important to make compar-

isons between maternal and offspring body masses across

the experiments and the long-term feeding manipulation.

Our study is based on planned comparisons, and the

predictions can then be tested statistically by estimating

two effects: (1) the main effect of experimental manip-

ulation (i.e., July body mass for control vs. treatment),

and (2) the two-way interaction between manipulation

and season (e.g., the increase in body mass from July to

September for control vs. treatment; Fig. 1). Conse-

quently, manipulation and its interaction with season

were kept in all candidate models based on our a priori

expectations (see e.g., Anderson et al. [2001], Burnham

and Anderson [2002] for extensive reviews of the theory

behind the model selection philosophy adopted in the

present study). Thus, we started with a model containing

all of the predictors and two-way interactions between

experimental manipulation and the other predictors.

From this model, we formed a pool of candidate models

in which all covariates and interactions were removed

sequentially (Appendix: Table A1). From this pool of

models, we selected the model with the lowest Akaike’s

Information Criterion (AIC) value (e.g., Burnham and

Anderson 2002). Following Pinheiro and Bates (2000),

maximum likelihood fitted models were used when

models were compared to each other (Appendix: Table

A1), whereas a restricted maximum likelihood fitted

model was used for parameter estimation. Because this

study consists of planned comparisons with well-defined

control groups, we used the treatment contrast, compar-

ing treatment to control, and Wald statistics to test the

hypothesis that the contrasts were not significantly

different from zero (see Pinheiro and Bates [2000] for

details). All statistical tests in this study were two-tailed,

and the null hypothesis was rejected at a ¼ 0.05.Generalized linear models (GLM) with a binary

response variable (0¼ absent, 1¼ present), using a logitlink function and a binomial distribution, were applied

in order to quantify female reproductive success (i.e., theprobability that a female had calf present in the autumn)

as a function of experimental manipulation, year, andinitial body mass (Crawley 2003). A dog intruded thecalf paddock in 2004, killing at least two of the calves in

the manipulation group in the long-term feedingmanipulation and in the improved winter conditions

treatment. Hence, we excluded data from 2004 in theanalyses of calf production in the two analyses. We

adopted the same model selection procedure as in theanalyses of body mass, except that season and its

interaction with manipulation were not included aspredictors in these analyses (Appendix: Table A2).

RESULTS

Long-term feeding manipulation

Improved winter feeding conditions did not have anylarge effect on female body mass the following July,September, and January (Table 1a). In contrast, we did

find a significant positive effect of improved feedingconditions on calf body mass (Table 1b). Mean body

mass was lower in 2004 compared to 2003 for bothfemales and calves, and the effect of year was quite

pervasive in all of the analyses presented. Interestingly,the year effect on body mass in calves was larger than

that of females (Table 1). The main effect of initial bodymass on female body mass was positive and statistically

significant (Table 1a). The effect of initial maternal bodymass on calf body mass was small and statistically

insignificant in the control group. However, we found apositive interaction between long-term feeding and

initial maternal body mass on calf body mass (Table1b), indicating that larger females allocated more to

their calves compared to smaller females in the long-term feeding group only. Long-term feeding did have asmall, statistically insignificant effect on calf production

(Table 2a), even though the direction of this estimatewas positive as expected. Nevertheless, the estimated

proportion of females with a calf was high across thetwo groups (the herd utilizing natural pastures had the

lowest estimate; probability 0.72). To summarize,females experiencing long-term improved winter condi-

tions increased their reproductive allocation in regard tocalf body mass, which means that they adopted a risk-

sensitive reproductive allocation, and this increasedallocation appeared to be especially pronounced in

initially large females.

Improved winter conditions (Experiment I)

Although females and calves tended to be larger afterone winter with improved conditions, the estimated

differences were small and nonsignificant after adjustingfor covariates (year, season, and initial female body


mass; Table 3, Fig. 2a). Initial body mass had a positive

effect on female body mass (Table 3a), but initial

maternal body mass did not have a strong effect on calf

body mass (Table 3b). This lack of an effect on calf body

mass indicated either that reproductive allocation was

higher for smaller relative to larger females (as calf body

mass was independent of initial maternal body mass), or

that winter body mass was a poor predictor of

reproductive performance. Experimental feeding did

not have a statistically significant effect on calf

production (Table 2b), even though the direction of this

estimate was positive as expected. In summary, these

results agreed with the risk-averse reproductive alloca-

tion hypothesis: females are unwilling to increase their

reproductive allocation during summer as a response to

occasionally good winter conditions.

TABLE 1. Estimates from linear mixed-effect models (LME) relating (a) female and (b) calf body mass to long-term feedingmanipulation, season (July, September, and January), and year (2003 and 2004).

Parameter

a) Female body mass andlong-term feeding

b) Calf body mass andlong-term feeding

Value 95% CL df P Value 95% CL df P

Fixed effects

Intercept 63.50 62.15, 64.85 105 22.62 21.21, 24.03 69Manipulation (improved) 1.19 �0.50, 2.87 73 0.17 3.12 1.31, 4.94 55 ,0.01Year (2004) �2.30 �3.68, �0.93 73 ,0.01 �4.97 �6.44, �3.49 55 ,0.01Season (September) 11.73 10.50, 12.95 105 ,0.01 22.09 20.78, 23.41 69 ,0.01Season (January) 8.79 7.62, 9.96 105 ,0.01 21.28 20.01, 22.55 69 ,0.01Initial body mass�,� 0.70 0.59, 0.82 73 ,0.01 0.08 �0.08, 0.25 55 0.33Manipulation (imp.) 3 Season (Sep)� �0.07 �1.86, 1.72 105 0.94 0.26 �1.81, 2.33 69 0.80Manipulation (imp.) 3 Season (Jan)� �1.06 �2.77, 0.65 105 0.22 �0.27 �2.29, 1.75 69 0.79Manipulation (imp.) 3 Initial body mass�,� . . . . . . . . . . . . 0.28 0.02, 0.54 55 0.04

Random effects: female§

Among-females standard deviation 2.55 2.03, 3.20 2.26 1.69, 3.01Within-females standard deviation (residuals) 2.35 2.05, 2.68 2.21 1.87, 2.61

Notes: The long-term feeding manipulation (improved) consisted of supplementary feeding in winter. The intercept shows theJuly 2003 body mass for control females (i.e., females utilizing natural pastures), whereas the other coefficients are the estimateddifference between the intercept and the mean body mass for each level of the other included factors. To make the interceptbiologically meaningful, initial body mass was centered (subtracting the average body mass). Body mass of females and calves wasmeasured in kilograms. Estimated parameters are for a model selected from a pool of candidate models (see Appendix andMethods: Statistical analyses for details on the model selection procedure applied). Ellipses indicate that the term was removedbecause it did not improve the model fit using AIC for model selection.

� Maternal body mass in January (i.e., before onset of manipulation) in both years.� Removal of nonstatistically significant interactions did not affect the remaining coefficients.§ Female random terms involved only the constant term (i.e., random intercepts fitted per female). For female body mass (a),

among-females nObs¼ 186; within-females nInd¼ 77. For calf body mass (b), among-females nObs¼ 133; within-females nInd¼ 60,where nObs is the number of observations and nInd is the number of individuals observed.

TABLE 2. Generalized linear model relating calf production to experimental manipulation (improved in the long-term feedingmanipulation and in Experiment I, and reduced in Experiment II) and year (2003 and 2004).

Parameter

Calf production and manipulation

Value 95% CL df P

a) Long-term feeding manipulation�Intercept 0.96 �0.02, 2.09Manipulation (improved) 1.53 �0.47, 4.56 29 0.19Residual deviance 28.32 29

b) Improved winter conditions� (Experiment I)

Intercept 0.96 �0.02, 2.09Manipulation (treatment) 0.51 �1.09, 2.25 32 0.54Residual deviance 36.71 32

c) Reduced winter conditions (Experiment II)

Intercept 1.96 0.78, 3.42Manipulation (treatment) �0.38 �1.69, 0.90 54 0.57Year (2004) �0.98 �2.42, 0.30 53 0.15Residual deviance 58.24 53

Notes: The intercept is the logit estimate for the control group in 2003. Calf production is the probability of producing a calf, as abinary response (i.e., a GLM with binomial family and a logit link function). See Appendix and Methods: Statistical analyses fordetails on the model selection procedure applied.

� Data from the year 2004 were removed from these analyses because a dog invaded the calf paddock, killing at least two calvesin one of the experimental groups.


Reduced winter conditions (Experiment II)

Experimentally reduced winter conditions had a

negative, nearly statistically significant effect on female

body mass in the following summer after controlling for

the effects of year and initial female body mass (Table

3a, Fig. 2b). Moreover, there was a significant positive

interaction between manipulation and season because

females experiencing a reduction in winter conditions

allocated more resources in somatic growth over the

summer than did control females (interaction term

manipulation 3 September season in Table 3a, Fig.

2b). There was a large effect of experimental manipu-

lation on calf body mass; the mothers that experienced

reduced winter condition gave birth to calves that were,

on average, ;4 kg smaller in July compared to mothers

that received supplementary feeding (Table 3b, Fig. 2b).

As no interaction between manipulation and season was

evident in the analysis of calf body mass, the calves of

the mothers that experienced reduced winter conditions

were smaller than the calves in the control group the

following September and January (Table 3b, Fig. 2b). In

contrast to the improved winter condition experiment,

initial maternal body mass did have a relatively strong

positive effect on calf body mass (Table 3b). Experi-

mental reduction in winter conditions and year had a

small, negative, and nonsignificant effect on calf

production (Table 2c). In summary, these results were

also in accordance with the risk-averse reproductive

allocation hypothesis: females reduced their subsequent

reproductive allocation as a response to reduced winter

feeding conditions.

DISCUSSION

In the present study we demonstrate that reindeer

adjusted their reproductive allocation during summer

TABLE 3. Linear mixed-effect models (LME) relating (a) female and (b) calf body mass to experimental translocation ofindividuals between the two herds, to seasons (July, September, and January), and to years (2003 and 2004).

Parameter

Improved winter conditions(Experiment I)

Reduced winter conditions(Experiment II)

Value 95% CL df P Value 95% CL df P

a) Female body mass (kg)

Fixed effects

Intercept 64.42 62.96, 65.88 106 64.32 62.92, 65.71 99Manipulation (treatment) 1.39 �0.42, 3.19 70 0.13 �1.71 �3.50, 0.08 69 0.06Year (2004) �3.01 �4.59, �1.43 70 ,0.01 �1.43 �2.91, 0.06 69 0.06Season (September) 11.76 10.56, 12.96 106 ,0.01 11.58 10.21, 12.96 99 ,0.01Season (January) 8.81 7.66, 9.95 106 ,0.01 7.64 6.33, 8.96 99 ,0.01Initial body mass� 0.60 0.46, 0.74 70 ,0.01 0.77 0.60, 0.95 69 ,0.01Manipulation (treat.) 3 Season (Sep)� 0.22 �1.58, 2.02 106 0.81 2.15 0.21, 4.08 99 0.03Manipulation (treat.) 3 Season (Jan)� �0.94 �2.58, 0.70 106 0.26 1.79 �0.06, 3.63 99 0.06Manipulation (treat.) 3 Initial body mass� . . . . . . . . . . . . �0.30 �0.55, �0.05 69 0.02



b) Calf body mass (kg)

Fixed effects

Intercept 22.51 20.88, 24.14 75 25.97 24.23, 27.72 52Manipulation (treatment) 0.73 �1.39, 2.86 50 0.49 �4.14 �6.28, �2.01 49 ,0.01Year (2004) �4.60 �6.41, �2.79 50 ,0.01 �5.19 �7.08, �3.31 49 ,0.01Season (September) 22.13 20.77, 23.50 75 ,0.01 22.44 20.91, 23.98 52 ,0.01Season (January) 21.28 19.97, 22.59 75 ,0.01 21.06 19.55, 22.57 52 ,0.01Initial body mass� 0.16 �0.01, 0.32 50 0.06 0.36 0.13, 0.59 49 ,0.01Manipulation (treat.) 3 Season (Sep)� 1.41 �0.66, 3.48 75 0.18 0.41 �1.73, 2.55 52 0.70Manipulation (treat.) 3 Season (Jan)� 0.49 �1.49, 2.47 75 0.63 0.71 �1.50, 2.91 52 0.52Manipulation (treat.) 3 Initial body mass�,� . . . . . . . . . . . . �0.11 �0.43, 0.20 49 0.47



Notes:Winter conditions were experimentally manipulated (improved in Experiment I and reduced in Experiment II) on a short-tem basis. The intercept shows the July 2003 body mass for control females, whereas the other coefficients are the estimateddifference between the intercept and the mean body mass for each level of the other included factors. To make the interceptbiologically meaningful, initial body mass was centered (subtracting the average body mass). See Appendix and Methods:Statistical analyses for details on the model selection procedure applied. Ellipses indicate that the term was removed because it didnot improve the model fit using AIC for model selection.

� Maternal body mass in January (i.e., before onset of manipulation) in both years.� Removal of nonstatistically significant interactions did not affect the remaining coefficients.§ Female random terms involved only the constant term (i.e., random intercepts fitted per female). For (a), among-females nObs¼

184 for ‘‘improved’’ and 177 for ‘‘reduced’’; within-females nInd ¼ 74 for both treatments. For (b), among-females nObs ¼ 133 for‘‘improved’’ and 110 for ‘‘reduced’’; within-females nInd¼ 54 for both treatments.


according to winter feeding conditions. When winter

conditions were reduced, females immediately reduced

their reproductive allocation the following summer,

presumably in order to not compromise their own body

mass at the onset of the next winter. In contrast, when

winter conditions were improved, females were reluctant

to increase their reproductive allocation. However,

females that had been provided additional winter forage

over several years allocated more in calves during

summer, indicating that reindeer can assess the predict-

ability of continuous winter conditions.

Critical issues in ecological experiments are whether

the applied treatment is relevant for addressing the focal

question, and if the level of treatment is realistic with

respect to that found in a natural setting. In our study it

is important that additional winter forage actually

improved winter conditions. Because females on natural

pastures were free-ranging during the winter, we were

unable to quantify the direct impact of additional forage

on female winter body mass. However, Fauchald et al.

(2004) showed that females given winter forage gained

;12 kg during winter, compared to their control

animals. Similar to Fauchald et al. (2004), the fed

females in this study were observed daily to ensure that

all individuals ingested forage and were in good health.

Although there was a difference between the two years

of the present study in terms of female and calf body

mass, indicating that the natural conditions in summer

differed, both winters were relatively benign, due to

shallow snow layers and no ice (Tveraa et al. 2007).

Thus, we could not expect a strong response to

additional winter feeding, especially in terms of calf

production, which is likely to be less sensitive than calf

body mass (Tveraa et al. 2003: Table 2). In the study by

Fauchald et al. (2004), female reindeer did not increase

their reproductive performance, despite the significantly

increased gain in body mass during winter. The

improved winter condition experiment replicates and

supports the findings of Fauchald et al. (2004) that

female reindeer regulate their body mass down to some

minimum threshold during spring when the risk of

starvation is low. Because responses to both long-term

improvement and short-term reduction of winter forage

availability were demonstrated in the present study, we

are confident that the manipulation applied in the

present study worked as we intended.

The herd receiving additional winter forage for several

years had larger calves. Interestingly, female body

masses did not differ between herds. In addition to

increased reproductive allocation, additional winter

feeding is also supposed to increase the growth of

subadults, which may greatly affect adult performance

and induce a cohort effect (Rose et al. 1998, Lindstrom

1999, Coulson et al. 2001, Forchhammer et al. 2001,

Lummaa and Clutton-Brock 2002, Gaillard et al. 2003).

Indeed, the females in the herd receiving the long-term

additional winter forage grow faster and reach maturity

earlier (T. Tveraa, P. Fauchald, K. Langeland, and B.-J.

Bardsen, unpublished data). Improved winter conditions

thus act to increase reproductive allocation at all ages

while body mass is kept constant. Generally, larger

females seem to outperform smaller females, which is

reflected in the general positive relationships between

initial female body mass and later maternal and

offspring body mass. The positive relationship between

maternal and offspring body mass can be used to

support the hypothesis that initially larger females have

a more risk-prone reproductive allocation relative to

smaller females. However, this interpretation is inaccu-

rate because even though initially larger females

produced larger calves, they also had a larger autumn

body mass compared to smaller females (van Noordwijk

and de Jong [1986] discuss how positive relationship

between two traits subject to trade-offs might occur).

When reproduction competes with the amount of

resources available for survival during an unpredictable

FIG. 2. Estimated maternal (left-hand axis; black solid orblack outlined symbols) and offspring (right-hand axis; graysolid or gray outlined symbols) body mass (mean 6 SE) foreach experimental group for each season (July, September, andJanuary) in 2003 for experimentally (a) improved and (b)reduced winter feeding conditions based on the analyses inTable 3.


nonbreeding season, then individuals should adopt what

we have termed a risk-sensitive reproductive allocation

(see also Boyce 1979, Boyce and Daley 1980, Erikstad et

al. 1998, Lindstrom 1999). Long-lived animals, such as

reindeer, are expected to be particularly risk sensitive. A

risk-averse reproductive allocation implies an asymmet-

ric response to environmental change in the sense that

females should be more responsive to reductions than to

improvements of the environment. Accordingly, rein-

deer in the present study readily reduced their repro-

ductive allocation when winter conditions were reduced,

whereas they more slowly increased their reproductive

allocation when winter conditions were improved.

Moreover, according to the risk-averse allocation

hypothesis, females should adjust their reproductive

allocation according to winter conditions that are below

average conditions (Boyce and Daley 1980, Stephens

and Krebs 1986). The increased reproductive allocation

of female reindeer as a response to additional feeding

over several years can be understood in light of this

prediction, because long-term feeding implied both an

increased average and a reduced variance in winter

conditions.

Ecological questions should be assessed with an

analytical approach that combines statistical analyses

of observational data, experiments, and mathematical

models (e.g., Turchin 1995). Research on large wild

mammals has typically been based on long-term

observational data, with a lack of experimental evidence

(e.g., Caughley 1981, Gaillard et al. 1998). Carefully

designed experiments based on marked individuals may

reveal mechanisms that cannot be reliably understood

based on nonexperimental study protocols (sensu, e.g.,

Festa-Bianchet and Jorgenson 1998, Gaillard et al.

1998). For example, many recent analyses of climatic

effect signatures in population time series have been used

to infer the likely consequences of future climate change

(Stenseth et al. 2002). The predicted consequences

commonly invoke more frequent population collapses

(e.g., Post 2005). Such inferences are based on an

underlying assumption that animals have a nonplastic

life history strategy that is not adequately adaptive to

new climate regimes. However, animals may indeed be

able to respond to changes in the environments by

adjusting their reproductive allocation, as we have

shown for subarctic reindeer. Thus, reindeer populations

may be more resilient than previously thought (cf.

Tveraa et al. 2007). For example, climate change is

expected to increase the amount of snow and ice on

reindeer winter pastures (Iversen 2003), thereby reducing

the winter conditions for the herds. Contrary to recent

studies (e.g., Post 2005), we expect these changes to

result in a more risk-averse life history that will buffer

the negative effects of climate (see also Tveraa et al.

2007). Consequently, we propose that future studies

should focus more on how long-lived organisms, such as

large terrestrial herbivores, adjust their life history to

counteract climate changes. In particular, we believe that

a valuable new focus in life history studies would be to

investigate how environmental stochasticity has shaped

the degree of risk-sensitive reproductive strategies.

ACKNOWLEDGMENTS

The present study was funded by the Research Council ofNorway. We thank Alf and Anna R. Johansen, Johannes A. P.and Ravna A. Guttorm, as well as Einar and Karin B. G.Pedersen and their respective families, for allowing us to usetheir animals in our experiments and for assisting us in the fieldat various circumstances. Various discussions with John A.Henden, Øystein Varpe, Audun Stien, Marius W. Næss, andJan O. Bustnes, as well as thoughtful comments from Jean M.Gaillard and several anonymous referees, have improved themanuscript. Rolf Rødven, Øystein Varpe, Ingrid Jensvoll, GuroSaurdal, and Linda L. Aune helped us with the fieldwork.

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Tveraa, T., P. Fauchald, C. Henaug, and N. G. Yoccoz. 2003.An examination of a compensatory relationship betweenfood limitation and predation in semi-domestic reindeer.Oecologia 137:370–376.

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APPENDIX

Model selection and the pool of candidate models (Ecological Archives E089-046-A1).

SUPPLEMENT

Raw data used in statistical analyses of risk-sensitive reproductive allocation in reindeer (Rangifer tarandus) (Ecological ArchivesE089-046-S1).


Ecological Archives E089-046-A1

Bård-Jørgen Bårdsen, Per Fauchald, Torkild Tveraa, Knut Langeland, Nigel Gilles Yoccoz, and Rolf Anker Ims. 2008. Experimental evidence of a risk-sensitivereproductive allocation in a long-lived mammal. Ecology 89:829–837.

Appendix A. Model selection and the pool of candidate models.

TABLE A1. The relative evidence for each candidate model (i) in Table 1 (Long-term feeding) and Table 3 (Experiment I and II) was assessed by rescaling and ranking models relative to the value of themodel with the lowest Akaike’s Information Criterion value (Δi; the model in bold were selected and used for inference in each analysis as its Δi equals zero). The models were fitted by maximumlikelihood (ML) as the restricted maximum likelihood (REML) fit used in the Table 1 and 3 are not recommended when several models are compared to each other (Pinheiro and Bates 2000). Thepredictors included in the different models are marked with an "x".

i

Manipulation† Season† Manip. × seas.† Year Initial body mass(IBM) Manip. × IBM Manip. × Year df

Female body mass, Δi Calf body mass, Δi Long-term

feeding

Experiment I

Experiment II Long-term

feeding

Experiment I

Experiment II

1. x x x x x x x 12 2.20 3.51 0.73 1.80 2.85 0.89 2. x x x x x x 11 0.37 1.70 0.00 0.00 1.43 0.00 3. x x x x x 10 0.00 0.00 4.02 2.90 0.00 0.35 4. x x x x 7 85.08 53.26 66.85 10.39 12.42 2.14 5. x x x 6 89.12 68.81 67.87 37.10 31.43 26.14

† The three predictors in bold were kept in all models based on our a priori expectations of the experimental translocation of animals in the three seasons of interest, i.e., we aimed at estimating the effectof experimental manipulation in the three different seasons.

TABLE A2. The relative evidence for each candidate model (i) in Table 2 was assessed by rescaling and ranking models relative to the value of the model with the lowest Akaike’s Information Criterionvalue (Δi; the model in bold were selected and used for inference in each analysis as its Δi equals zero). Season was not included as a predictor in these analyses as updated calf presence in the autumn wasused as a proxy for production throughout all seasons. The predictors included in the different models are marked with an "x".

i

Manipulation† Year Initial body mass(IBM) Manip. × Year Manip. × IBM df

Calf production, Δi Long-term

feeding‡

Experiment I‡ Experiment II

1. x (x) x (x) x 6(4) 1.65 2.73 3.13 2. x (x) x (x) 5 __ __ 1.15 3. x (x) x 4(3) 1.99 1.91 0.43 4. x (x) 3 __ __ 0.00 5. x 2 0.00 0.00 0.23

† The predictor in bold was kept in all models based on our a priori expectations of the experimental translocation of animals, i.e., we aimed at estimating the effect of experimental manipulation.‡ Data from the year 2004 was removed from two analyses as a dog intruded the calf paddock killing at least two calves in one of the experimental groups. Consequently, the terms including year werenot included in these models (the markings not included as well as the degrees of freedom for these analyses are given in parentheses).

LITERATURE CITED

Pinheiro, J. C., and D. M. Bates. 2000. Mixed effect models in S and S-PLUS. Springer, New York, USA.

[Back to E089-046]

Ecological Archives E089-046-A1 http://www.esapubs.org/archive/ecol/E089/046/appendix-A.htm

1 of 1 31.03.2008 13:25

PAPER 2

Experimental evidence of costs of lactation

in a low risk environment for a long-

lived mammal

Bårdsen, B.-J., P. Fauchald, T. Tveraa, K. Langeland & M. Nieminen

Oikos: in press

Experimental evidence of costs of lactation in a low risk environmentfor a long-lived mammal

Bard-Jørgen Bardsen, Per Fauchald, Torkild Tveraa, Knut Langeland and Mauri Nieminen

B.-J. Bardsen ([email protected]), P. Fauchald, T. Tveraa, K. Langeland and M. Nieminen, Norwegian Inst. for Nature Research (NINA), Div. ofArctic Ecology, Polar Environmental Centre, NO-9296 Tromsø, Norway. BJB, PF and KL also at: Dept of Biology, Univ. of Tromsø (UIT),NO-9037 Tromsø, Norway. MN also at: Finnish Game and Fisheries Research Inst., Reindeer Research Station, FI-99910 Kaamanen, Finland.

In a previous experiment we have documented that organisms adopt a risk-sensitive reproductive allocation when summerreproductive investment competes with survival in the coming winter (Bardsen et al. 2008). This tradeoff is presentthrough autumn female body mass, which acts as an insurance against unpredictable winter environmental conditions.We tested this hypothesis experimentally on female reindeer experiencing stable and benign winter feeding conditions.Additional supplementary feeding and removal of newborns represented two sets of experimental manipulations. Femalesin the supplementary feeding group increased more in winter body mass relative to control females. This manipulation,however, did not have any effect on summer body mass development for neither females nor offspring, but we found apositive effect of feeding on offspring birth mass for smaller females. In contrast, offspring removal did have a positiveeffect on summer body mass development as females in this group were larger in the autumn body mass relative tocontrol females. In essence, we documented two immediate effects as: (1) supplementary feeding did have a positive effecton spring body mass for smaller females; and (2) offspring removal did increase the female summer somatic growth as thishad a positive effect on female autumn body mass. Additionally, we tested for lagged effects, but we could not documentany biologically significant effects of neither manipulation in the coming spring. The fact that we only found rather weakeffects of both manipulations was as expected for risk sensitive individuals experiencing benign environmental conditionsover many years.

A central issue in life-history theory is how individualsbalance reproductive investments against their own chancesto survive and reproduce in the future (Stearns 1992, Daanand Tinbergen 1997, Stearns and Hoekstra 2000). Thistradeoff between current reproduction and future survivaland reproduction is more commonly referred to as the costof reproduction (sensu Williams 1966), and this cost canroughly be divided in two: immediate, where individualspay the costs during nurturing; and delayed, whereindividuals pay the costs post offspring maturation. Delayedcost of reproduction can for mammalian females be dividedin two: (1) post-lactational parental care; and (2) maternalrecovery, whereas immediate costs can be divided in three:(1) mating; (2) gestation (including conception andparturition); and (3) lactation (reviewed by Gittleman andThompson 1988). Biologists have for a long time believedthat the cost of lactation is large relative to that of otherreproductive stages but most studies have focused ongestation vs lactation (Gittleman and Thompson 1988):e.g. humans Homo sapiens and other primates (Anderson1983, Bronson 1995, Dufour and Sauther 2002, Ellison2003), large terrestrial herbivores; moose Alces alces (Sand1998), reindeer/caribou Rangifer tarandus (Reimers 1983,Cameron et al. 1993, 2002) and red deer Cervus elaphus

(Clutton-Brock et al. 1989), as well as rodents; Guinea pigCavia porcellus (Kunkele 2000).

Reproductive patterns exhibit large interspecific variation(Stearns 1992, Coulson et al. 2000), but for large mammalsa surprisingly large intraspecific variation between popula-tions and even between individuals is apparent (Sand 1996,Sæther et al. 1996). Environmental factors are believed to beof special importance in explaining variation in reproductiveperformance among populations (Tveraa et al. 2007), andeven within the same population over time (Bardsen et al.2008). For large herbivores living in the Northern Hemi-sphere, late winter feeding conditions have profound effectson both survival and reproduction (Coulson et al. 2000,2001, Patterson and Messier 2000, DelGiudice et al. 2002).Thus, different environments favour different traits, and intemporally variable environments animals traits will changeaccordingly (Sæther 1997, Festa-Bianchet and Jorgenson1998, Forchhammer et al. 2001, Gaillard and Yoccoz 2003,Adams 2005, Bardsen et al. 2008). Such changes can involvephenotypic plasticity, which are of considerable interest inorder to predict potential climate-effects (Sæther et al. 2000,Stenseth et al. 2002).

Most large terrestrial herbivores in northern ecosystemsare considered capital breeders (Festa-Bianchet et al. 1998),

Oikos 000: 1�16, 2008

doi: 10.1111/j.1600-0706.2008.17414.x,

# 2008 The Authors. Journal compilation # 2008 Oikos

Subject Editor: Tim Benton. Accepted 11 December 2008

1

because they rely, at least partly, on accumulated bodyreserves for reproduction (Jonsson 1997, Stearns 1992).Capital and income breeding strategies represent options atextreme ends of a continuous distribution of choices forenergy use defined by foraging decisions, and theory predictsthat an organism’s breeding strategy will have importantconsequences for its fitness. Capital breeders should adopt arisk sensitive reproductive allocation strategy when repro-duction competes with the amount of resources available forsurvival during an unpredictable non-breeding season (sensuBardsen et al. 2008). For large terrestrial herbivores innorthern and mountain environments reproduction gener-ally takes place during the favourable season (summer),whereas survival is particularly constrained in the unfavour-able season (winter: Sæther 1997). In these environmentsindividuals should retain sufficient body reserves in theautumn as to ensure survival during especially harsh winters(Erikstad et al. 1998). Individuals, thus, trade the amount ofresources to allocate in their own body reserves against theamount of resources to allocate in reproduction duringsummer, where the latter affect an individual’s autumn bodyreserves negatively (Bardsen et al. 2008).

Animals should respond more strongly to deteriorationthan to improvement of environmental conditions (Bardsenet al. 2008). This can be exemplified as follows: for a givendistribution of winter conditions, a risk prone reproductivestrategy involves high reproductive allocation that will resultin high reproductive reward during benign winters, buthigh survival cost during harsh winters. A low reproductiveallocation will, on the other hand, result in stable wintersurvival but lower reproductive reward. This represents arisk averse reproductive strategy. Additionally, Bardsen et al.(2008) argues that when benign winter conditions appearover several years, individuals should increase their repro-ductive allocation. This is because the amount of autumnbody reserves needed as insurance against winter starvation

is lowered under benign conditions. This reasoning issupported empirically by the fact that many organisms areable to buffer their reproductive strategies according toenvironmental factors: mammals; e.g. humans (Bronson1995, Lycett and Dunbar 1999, Quinlan 2007), Rangifer(Adams 2005, Tveraa et al. 2007, Bardsen et al. 2008),bighorn sheep Ovis canadensis (Festa-Bianchet and Jorgen-son 1998) and Weddell’s seals Leptonychotes weddellii(Hadley et al. 2007), and long-lived birds (theoreticalapproach: Drent and Daan 1980, Erikstad et al. 1998); e.g.Antarctic petrel Thalassoica antarctica (Varpe et al. 2004).

In this study, we set up an experiment in sub-arcticFinland designed to test predictions about costs of lactationunder benign winter feeding conditions for reindeer. InJanuary 2007, we allocated females between four experi-mental groups consisting of two treatments (Fig. 1): (1)environmental manipulation with control animals onnatural pastures and one group where individuals receivedsupplementary winter feeding (supplementary feeding; SF);and (2) reproductive manipulation with control animalswho lactated and one group where offspring was removed0�2 days after parturition (lactation; LA). Immediate costsof reproduction, i.e. the lactation period, was measured byindividual survival and seasonal development in body mass,whereas the relationship between maternal and offspringbody mass was used as a measure of maternal allocation.Delayed costs of reproduction, i.e. the post-lactationalperiod, was measured by body mass of females and theirnewborn offspring in the spring the year following experi-mental manipulation.

This experiment will give us answers to the followingquestions: (1) what is the immediate cost of reproductionunder different environmental conditions during lategestation for female reindeer in the spring (‘immediateeffects of manipulated winter conditions’) versus in theautumn (‘summer somatic allocation’)? (2) How does

Naturalpastures (CO)

Supplementary feeding (SF )

CO

Time

nTotal = 72

SF

CO

SF

January February - April May June October

Measurement of response

FinalizationInitiation

environmentNo offspring removal (CO)

Offspring removal (LA)

CO

CO

LA

LA

reproductionDesign

conditions

Groups together

SF - CO

CO - LA

SF - LA

SF - CO

CO - LA

SF - LA

Manipulation

CO - CO

CO - LA

SF - LA

SF - CO

nGroup = 18

CO - CO CO - CO

Groups together

+ +

Figure 1. The study was designed with respect to initial body mass, i.e. pre-manipulative body conditions measured at the 8 January, of72 pregnant females (�). These were allocated to each experimental groups (n�18 per group) following a stratified-randomized designalgorithm. Manipulation of feeding conditions (CO; ‘control’ on natural pastures and SF; ‘supplementary feeding’) was performed inwinter whereas manipulation of reproduction (CO; ‘control’ who kept their offspring and LA; manipulation of lactation by offspringremoval 0�2 days after birth) was performed in the spring.

2

female reproductive status (‘barren’ vs ‘lactating’) affectfemale body condition in the autumn (‘summer somaticallocation’)? (3) How does environmental conditions duringgestation affect female reproductive allocation and offspringbody condition in the spring (‘immediate effects of winterconditions’) versus in the autumn (‘summer reproductiveallocation’)? (4) To what extent does delayed, i.e. lagged,effects of environmental and reproductive manipulationaffect female and offspring body condition and birth date inspring of the year following the experiment (‘delayed costsof reproduction’)?

Methods

Study area and the experimental reindeer herd inKaamanen, Finland

The study was carried out in Kaamanen ExperimentalReindeer Station (698N, 278E), where a herd of �80females with known life histories has been monitored forseveral decades (Holand et al. 2006, Weladji et al. 2006,Røed et al. 2007). The total study area of 43.8 km2 isfenced and sub-divided into several smaller enclosures usedon a seasonal basis, and within enclosures reindeer are freelygrazing on natural pastures except for the calving season(May to early June) in which they are kept within a calfpaddock (�8 ha in size). From 15 January to 30 April asubset of the herd, the supplementary feeding group, wasgiven 2 kg individual�1 day�1 in the form of commercialreindeer pellets (Poron-Herkku, Rehuraisio, Finland). An-other subset of the herd, the natural pastures group, wasgiven feeding in the form of 200 g individual�1 day�1.During a usual winter, reindeer in Kaamanen are given �2kg hay and concentrate, i.e. �0.5 feeding units, in-dividual�1 day�1 from January to April. This equals46% of the daily feeding requirements of reindeer as theyrequire �1.1 feeding units day�1 (Nieminen unpubl.).Population density may in interaction with the environ-ment affect the reindeer’s perception of the environment(Bardsen et al. unpubl.), but reindeer density within theareas has been stable over years due to autumn slaughtering(2004�2008: mean�2.8 individual�1 km�2 (range�2.6�2.9)).

Experimental protocol

On 8 January 2007 animals were gathered, their gestationalstatus (‘pregnant’ or ‘barren’) and body mass were recorded.Gestational status was assessed with an ultrasound scanner(with a 7.5 MHz rectal probe, measures taken by veterinaryHeikki Sirkkola, Hameenlinna, Finland), and only preg-nant females were included in the experiment. From thissubsample of data individuals were assigned to one of twoexperimental manipulations (four experimental groupstotally; Fig. 1): (1) environmental manipulation; (1a)control females on natural pastures (control) and (1b)manipulation of winter conditions by supplementary feed-ing. (2) Reproductive manipulation; (2a) control femalesthat were lactating (control) and (2b) manipulation oflactation by offspring removal 0�2 days after parturition.Initial female body mass, i.e. pre-manipulative body

conditions, a potentially confounding covariate (Kojola1993, Clutton-Brock et al. 1996, Festa-Bianchet et al.1998, Tveraa et al. 2003, Adams 2005, Bardsen et al.2008), was equally distributed across the experimentalgroups by performing a stratified-randomized design(Fauchald et al. 2004). First, 72 females were sortedaccording to their body masses. Second, 18 strata ofapproximately similar body masses were formed. Third,individuals within each stratum were randomly allocated toeach experimental group (sensu A1). Individual body massand presence (‘present’ or ‘absent’) were in 2007 (whenassessing immediate effects) recorded on gatherings on 5March, 14 April, 5 June and 22 October (Fig. 1), whereasin 2008 (when assessing delayed effects) this informationwas measured on the 23 April. Individual body mass wasrecorded to the nearest 0.1 kg using an electronic balance.During the calving season newborns were caught by hand,individually marked and their body mass and sex wasrecorded. Date of birth (1�1 May, 2�2 May, . . . , k�kdays from 1 May) as well as female reproductive status(‘reproducing’ or ‘barren’) was also recorded. The calvingarea was visited daily.


Missing values, survival, reproductive success and initialfemale body massNone out of 284 female body masses were missing, but 4 of66 offspring body masses were missing from June toOctober 2007. One female in the offspring removal groupshad a calf in the autumn and was thus removed from theanalyses. The effect of missing values on initial female bodymass was, thus, considered to be practically unimportant(sensu Bardsen et al. 2008). Two females did not give birth(both in the same experimental group; supplementaryfeeding with no offspring removal) and one female’sreproductive status was unknown in 2007. Such a highreproductive success rate (1.0 in three groups and 0.9 in onegroup; ngroup�18) makes it impossible to relate reproduc-tive success to experimental manipulation or initial femalebody mass. All individuals survived until October (twooffspring body masses were missing in October), whichagain means that it was impossible to relate survival to anyof the above mentioned variables. In 2008, two females didnot give birth and one female’s reproductive status wasunknown (all in the same experimental group; females withno offspring removal on natural pastures in the precedingwinter). Moreover, 12 females were missing in 2008 due toslaughtering of animals in October 2008. Two animalswhere lacking in each of the natural pasture experimentalgroups, whereas four animals where lacking in each of thetwo supplementary feeding experimental groups

We tested the design and found no statistically significantdifferences between the experimental groups for initial femalebody mass and age (Appendix A1). Initial female body massand age were highly correlated for younger females (54years; Pearson’s product-moment correlation, r�0.84 (0.57,0.95; DF�13)), but not for older ones (�4 years; r�0.09(�0.19, 0.34; DF�53)). Moreover, no senescent indivi-duals (maximum age was 13 years; nfemales B11 years�5) andfew young individuals (nfemales �4 years�12) were includedin the study. Consequently, we did not include age in anyfurther analyses. All statistical analyses were carried out in R

3

(R Development Core Team 2007Bhttp://www.R-project.org�).

Immediate effects � responses to experimentalmanipulations within 2007

Allocation in reproduction vs somatic growth: female andoffspring body mass. Linear mixed-effect models (LME)applied using the NLME package (Pinheiro and Bates2000, Pinheiro et al. 2008) were used to analyze the effectof the predictors on body mass of the females and offspring.For females, experimental manipulation of environment(control and supplementary feeding) and reproduction(control and lactation), initial female body mass (Januaryprior to manipulation) and season (March, April, June andOctober) were applied as fixed effects (Fig. 1), whereasfemale identity was included as a random effect (Pinheiroand Bates 2000). All mixed effect-models in the presentstudy were fitted with random intercepts only.

In order to assess the cost of lactation under differentwinter conditions it was important to make comparisonsbetween maternal and offspring body masses. Our study isbased on planned comparisons, and the predictions canthen be tested statistically by estimating the followingeffects: (1) the main effect of environmental manipulation(supplementary feeding); (2) the main effect of reproductivemanipulation (lactation); (3) the main effect of season; (4)the two-way interaction between supplementary feedingand lactation; (5) the two-way interaction between supple-mentary feeding and season; (6) the two-way interactionbetween lactation and season; and (7) the three-wayinteraction between supplementary feeding, lactation andseason. In sum, it is important to estimate the difference inbody mass for the different experimental groups across thefour different seasons. Consequently, the above mentionedpredictors were kept in all candidate models based on our apriori expectations (for extensive reviews of the theorybehind the model selection philosophy adopted in thepresent study see Anderson et al. 2001, Burnham andAnderson 2002). Thus, we started with a model containingall the above predictors and two-way interactions betweenthe two experimental manipulations and the other pre-dictors. From this model, we formed a pool of candidatemodels where all covariates (initial body mass and the sex ofthe offspring born in 2007) and interactions were removedsequentially (Appendix A2: Table A2.1). From this pool ofmodels we selected the model with the lowest Akaike’sinformation criterion (AIC) value (Burnham and Anderson2002). Following Pinheiro and Bates (2000) maximumlikelihood fitted models were used when models werecompared to each other (Appendix A2), whereas a restrictedmaximum likelihood fitted model was used for parameterestimation. For offspring we included manipulation ofenvironment (control and supplementary feeding) and allabove mentioned predictors except those including repro-ductive manipulation (the offspring removal groups did notcontain any reproductive data so we removed it). As thisstudy consisted of planned comparisons, with well-definedcontrol groups, we used the treatment contrast comparingtreatment to control, and Wald statistics to test thehypothesis that the contrasts were not significantly differentfrom zero (Pinheiro and Bates 2000). All statistical tests in

this study were two-tailed, the null-hypothesis was rejectedat an a-level of 0.05.

Spring reproductive allocation: birth mass and date.Linear models (LM) were used to analyze the effect ofenvironment manipulation (control and supplementaryfeeding) and initial female body mass on birth date andbirth mass of the offspring. For the residuals in the analysesof birth date to fulfill the normality assumption we squareroot transformed the response in this analysis includingboth the results presented in figures and tables. We adoptedthe same model selection procedure as in the analyses ofseasonal body mass development except that season and itsinteraction with manipulation were not included aspredictors in these analyses (Appendix A2: Table A2.2).

Delayed effects � responses to experimental manipulationsin 2008Allocation in reproduction vs. soma: female spring bodymass, offspring birth mass and birth date LM were used toanalyze the effect of experimental manipulation of environ-ment (control and supplementary feeding), manipulation ofreproduction (control and lactation) and initial female bodymass on spring female body mass, birth date and birth massof the offspring in the year following the experimentalmanipulations. We adopted the same model selectionprocedure as in the analyses of reproductive allocationabove except that the three-way interaction between thealready mentioned variables was included as predictors inthese analyses (Appendix A2: Table A2.3).

Results

Immediate effects � responses to experimentalmanipulations within 2007

Allocation in reproduction vs somatic growth: female andoffspring body massSupplementary feeding had a positive effect on female bodymass in March (main effect of supplementary feeding: 3.78kg, Table 1a). During winter and summer we did not findevidence of any effects of reproductive manipulation in theform of offspring removal (lactation) on female body mass asnone of the following estimates were statistically significant inMarch, April or June (Table 1a, Fig. 2a): (1) the main effectof lactation; (2) the two-way interaction between lactationand supplementary feeding; (3) the two-way interactionbetween lactation and season; and (4) the three-way interac-tion between lactation, supplementary feeding and season.Additionally, initially smaller females were smaller relative tolarger ones (initial body mass: 0.81 kg).

Reindeer on natural pastures gained on average 3.65 kgin body mass from January to April (main effect of April,Table 1a). Nevertheless, the relative difference between thefour experimental groups found in March, i.e. the positiveeffect of supplementary feeding, was constant throughoutwinter as none of the following estimates was statisticallysignificant for April (Table 1a): (1) the two-way interactionbetween supplementary feeding and season; (2) the two-wayinteraction between lactation and season; and (3) the three-way interaction supplementary feeding, lactation andseason. Consequently, the only real effect of manipulation

4

during winter was a general positive effect of supplementaryfeeding on female body mass, and this effect was additive orequal across the two groups (Table 1a, Fig. 2a). As foundpreviously, improved winter conditions did not have largepositive effects on female body mass the following summer(Fauchald et al. 2004, Bardsen et al. 2008). In fact, femalesin all experimental groups dropped to approximately similarbody mass in June (Table 1a, Fig. 2a).

A general increase in body mass from March to Octoberwas evident (main effect of October: 4.18 kg). In thisseason, however, several interesting statistical significantinteractions were present, making it evident that a shift inimportance from environmental towards reproductivemanipulation occurred. This is clearly evident in the visualrepresentation of the model (Fig. 2a), but it was formallytested by comparing the following effects: First, thesignificant negative interaction between season (October)and supplementary feeding of �3.87 kg was larger than themain effect of supplementary feeding. This simply meansthat the positive effect of supplementary feeding present inboth March and April had completely disappeared in the

autumn (Table 1a). Second, the significant negative inter-action between season (October) and lactation of 4.71 kgwas large compared to the small and non-significant maineffect of lactation, where the latter estimate represents howthis predictor affected female body mass in March. Thus, inOctober the offspring removal group was on average �4 kgheavier compared to the control group consisting oflactating females. Third, the lack of a large estimatedthree-way interaction between lactation, supplementaryfeeding and season means that the effect of lactation wasadditive within supplementary feeding across all seasons.For October, this means that the positive effect of offspringremoval was similar across the two environmental manip-ulation groups (females in the natural pastures andsupplementary feeding groups did not respond significantlydifferent to offspring removal).

In the analysis of offspring body mass development wefound no positive effect of supplementary feeding onneither summer (main effect of supplementary feeding:Table 1b) nor autumn body mass (interaction betweensupplementary feeding and season: Table 1b). This in-

Table 1. Estimates from linear mixed effect models (LME) relating female (a) and offspring (b) body mass to experimental manipulation ofwinter conditions (CO; ‘natural pastures’, and SF’; ‘supplementary feeding’) and experimental manipulation of lactation (CO; ‘lack ofoffspring removal’ and ‘LA’; ‘offspring removal’), season (March, April, June and October) and initial female body mass. The intercept showsMarch mass for control females. To make the Intercept biologically meaningful initial body mass was centered (subtracting the average bodymass). Estimated parameters are for a model selected from a pool of candidate models (Appendix 2 and Fig. 2).

Parameter Allocation in soma vs reproduction

Value (95% CI) DF p-value

(a) Female body mass (kg)a

Fixed effectsIntercept 76.83 [74.75,78.91] 197Environmental manipulation (SF) 3.78 [0.84,6.72] 65 0.01Reproductive manipulation (LA) �0.47 [�3.41,2.48] 65 0.75Season (April) 3.65 [1.19,6.10] 197 B0.01Season (June) �7.41 [�9.87,�4.96] 197 B0.01Season (October) 4.18 [1.72,6.63] 197 B0.01Initial body massb 0.81 [0.72,0.90] 65 B0.01Env. man. (SF)�Reprod. man. (LA) 0.28 [�3.88,4.44] 65 0.89Env. man. (SF)�Season (April) �0.20 [�3.63,3.22] 197 0.91Env. man. (SF)�Season (June) �2.53 [�5.96,0.89] 197 0.15Env. man. (SF)�Season (Oct.) �3.87 [�7.32,�0.42] 197 0.03Reprod. man. (LA)�Season (April) 0.19 [�3.24,3.61] 197 0.91Reprod. man. (LA)�Season (June) 1.13 [�2.29,4.56] 197 0.51Reprod. man. (LA)�Season (Oct.) 4.71 [1.29,8.14] 197 0.01Env. man. (SF)�Reprod. man. (LA)�Season (April) 1.19 [�3.65,6.04] 197 0.63Env. man. (SF)�Reprod. man. (LA)�Season (June) �0.90 [�5.74,3.95] 197 0.72Env. man. (SF)�Reprod. man. (LA)�Season (Oct.) 2.63 [�2.24,7.49] 197 0.29

Random effects: femalec

Among females standard deviation 2.40 [1.82,3.17] nObs.�279Within females standard deviation (residuals)c 3.63 [3.29,4.01] nInd.�70

(b) Calf body mass (kg)Fixed effects

Intercept 11.72 [8.95,14.49] 28Environmental manipulation (SF) �0.30 [�3.48,2.88] 27 0.85Season (October) 36.57 [33.8,39.35] 28 B0.01Offspring sex (male) 3.33 [0.65,6.02] 27 0.02Initial body massb 0.26 [B0.01,0.51] 27 0.05Env. man. (SF)�Season (October) �2.65 [�6.66,1.35] 28 0.18Env. man. (SF)�Initial body massb 0.03 [�0.31,0.36] 27 0.87

Random effects: femalec

Among females standard deviation 1.90 [0.73,4.96] nObs.�62Within females standard deviation (residuals) 3.83 [2.96,4.95] nInd.�32

aOne outlying observation (standardized residual��6.25) was excluded from the analysis. This exclusion did not affect the results notably.bMaternal body mass in January (i.e. before onset of manipulation).cFemale random terms involved only the constant term (i.e. random intercepts fitted per female).

5

dicates a lack of increased reproductive allocation for thefemales experiencing improved winter feeding conditions(Fig. 2b). Initially smaller females produced smaller off-spring relative to initially larger females, and this effect waspresent in both summer and autumn (main effect of initialbody mass: 0.29 kg, Table 1b). Moreover, male offspringwas larger than female offspring in both seasons (Table 1b).To summarize, females experiencing improved winterconditions invested more in somatic growth during latewinter, but they did not seem to translate this to increasedreproductive allocation during summer. On the other hand,manipulation of lactation did have a large effect on femalesomatic growth during summer.

Spring reproductive allocation: birth mass and dateAverage birth mass was not higher in the supplementaryfeeding group (main effect of supplementary feeding,Table 2a). Smaller females (572 kg) in the control groupon natural pastures produced significantly smaller offspringrelative to larger females (main effect of initial body mass:0.09 kg, Table 2a, Fig. 3a). This effect was, however, notpresent in the supplementary feeding group where asignificantly weaker effect of initial female body mass waspresent (interaction between supplementary feeding andinitial body mass: �0.07 kg, Table 2a, Fig. 3a). This meansthat the positive relationship between initial female bodymass and birth mass found for the control group on naturalpastures was not present for females in the supplementaryfeeding group. Average (squared root) birth date was not

related to manipulation (main effect of supplementaryfeeding: Table 2b). Smaller females in both groups gavebirth later relative to larger females (main effect of initialbody mass: �0.04 kg, Table 2b, Fig. 3b). To summarize,smaller females experiencing improved winter conditionsseemed to increase their reproductive allocation duringgestation, measured as increased birth mass, compared tosmaller females on natural pastures (Fig. 3a).

Delayed effects � responses to experimentalmanipulations in 2008

Allocation in reproduction vs soma: female spring bodymass, offspring birth mass and birth dateWe found no particularly strong effects of manipulation inthe year following the experiment: First, average femalespring body mass was not statistically different for eitherenvironmental or reproductive manipulation (main effect oflactation and supplementary feeding: Table 3a). Initiallysmaller females were still smaller the year after manipulationrelative to larger females (main effect of initial body mass:0.97 kg, Table 3a, Fig. 4a�b). This relationship was notstatistical significantly different between the two reproduc-tive manipulation groups (interaction between lactation andinitial body mass: Table 3a), but this relationship wasweaker for females in the supplementary feeding groupcompared to the control group on natural pastures(interaction between supplementary feeding and initialbody mass: � 0.30 kg, (Table 3a, Fig. 4a�b). Smallerfemales that received supplementary feeding the preceding

March April June October

68

75

82

89 (a) Female

Control Control

Supplementary feeding Offspring removal

Environmental manipulation Reproductive manipulation

(b) Offspring

June

10.0

11.3

12.7

14.0

October

43

46

49

52 (c) OffspringControl

Supplementary feeding

Environmental manipulation

Season

Mea

n bo

dy m

ass

(kg)

± S

E

Figure 2. Estimated mean maternal (a) and offspring (b�c) body mass for each experimental group in each season presented with91 SE(bars) based on the analyses presented in Table 1.

6

winter (12�14 months before) was, thus, larger compared tosmaller females on natural pastures. Second, average off-spring birth masses were not statistical significantly differentacross both types of manipulation (main effect of supple-mentary feeding and lactation: Table 3b, Fig. 4c�d). Againwe documented that larger females gave birth to largeroffspring the year following manipulation (main effect of

initial body mass: Table 3b, Fig. 4c�d). This shows thatfemale body mass in January 2007 was still a predictor ofbirth body mass 14�15 months ahead. Third, in the analysisof offspring birth date we found no delayed effects at all asneither manipulations or initial female body mass waspresent (Table 3c, Fig. 4e�f). To summarize, except for alagged positive effect of initial female body mass and a

Table 2. Estimates from linear models (LM) relating offspring birth mass (a) and birth date (b) to experimental manipulation of winterconditions (CO; ‘natural pastures’, and SF’; ‘supplementary feeding’) and initial female body mass. The intercept shows mass for controlfemales. To make the Intercept biologically meaningful initial body mass was centered (subtracting the average body mass). Estimatedparameters are for a model selected from a pool of candidate models (details in Appendix 2 and Fig. 3).

Parameter Reproductive allocation

Value (95% CI) p-value

(a) Offspring birth mass (kg)a

Intercept 6.25 [5.96,6.55]Environmental manipulation (SF) 0.15 [�0.28,0.57] 0.50Initial body massb 0.09 [0.05,0.13] B0.01Env. man. (SF)�Initial body massb �0.07 [�0.12,�0.01] 0.02

(adjusted R2�0.25, F�8.34, DF�3,63, pB0.01)

(b) Offspring birth date (days)c

Intercept 3.47 [3.14,3.80]Environmental manipulation (SF) 0.14 [�0.32,0.61] 0.54Initial body massb �0.04 [�0.07,�0.01] 0.01

(adjusted R2�0.08, F�3.72, DF�3,64, p�0.03)

aOne potential outlying observation, i.e. the birth mass of 9.2 kg, was detected, but as its removal did not affect the conclusion drawn fromthis analysis we kept it in the analysis.bMaternal body mass in January (i.e. before onset of manipulation).cBirth date, i.e. the number of days from 1 May, was square root transformed in order to approximate normally distributed residuals.Consequently, the reported estimates in this table are on square root scale.

-10

12 (a)

Con

tras

t for

birt

h m

ass

(kg)

10090807060

2

3

4

5

6

Initial female body mass (kg)

(b)Environmental manipulation

Control

Supplementary feeding

birt

h da

te (

days

)

Figure 3. Birth mass contrast between SF and control females (a), and birth date (b), square root transformed, in 2007 as a function ofinitial female body mass (8 January) and experimental group (birth mass; mean�6.32 kg91 SD, n�67 and birth date; mean�13.48days97.37 SD, n�67). This is a visualization of data and models with non-centered initial body mass presented in Table 2. Due tothe interaction shown in Table 2a we show the contrast, i.e. the difference, and 95% CI for the difference between the control and thesupplementary feeding groups (a). The plot showing the estimated difference between fed and control animals was produced using the‘estimable’ function in the ‘gregmisc’ library for R (Warnes 2008).

7

positive effect of supplementary feeding for smaller femaleswe found no biologically significant lagged effects.

Discussion

In the present study we demonstrated an immediate, but nodelayed, cost of reproduction for female reindeer asmanipulation of lactation resulted in a higher autumnbody mass, and this cost were not related to environmentalconditions during late gestation. We also found animmediate positive effect of winter feeding conditions onfemale body mass during late gestation, but this effect wasnot present in the following seasons within the same yearand in spring the following year. We found conflictingevidence of increased summer reproductive allocation dueto experimentally improved winter feeding conditions.First, we found no effect of supplementary feeding onJune or October offspring body mass. This indicates thatimproved winter conditions did not increase femalereproductive allocation during spring (from birth to June)or summer (from June to October) in 2007. Second, wefound that smaller females in the supplementary feedinggroup gave birth to larger offspring compared to controlfemales on natural pastures. This indicates that improvedwinter conditions lead to increased reproductive allocationfor smaller females. Third, we found a small delayed, or

lagged, effect of supplementary feeding on female bodymass for initially smaller females in the spring of 2008. Insum, even though the duration of the present study wasonly two years we documented a cost of lactation in theautumn and an effect of supplementary winter feeding onfemale winter and spring body mass and offspring birthmass within the same year as treatments were applied.

For ecological experiments it is always a critical issue ifthe applied manipulations are relevant for addressing thefocal question, and if the level of treatment is realistic withrespect to that found in a natural setting. Raising theseissues is redundant for manipulation of lactation as loosingoffspring, especially in the early phase of lactation, is quitecommon for many large terrestrial herbivores includingRangifer (Adams et al. 1995). Raising these issues forenvironmental manipulation is more relevant as the experi-ment were conducted within an experimental research herd(Holand et al. 2006) that has received supplementaryfeeding for years.

Supplementary winter feeding, using similar pellets asthe current study, has been applied in previous experiments(Fauchald et al. 2004, Bardsen et al. 2008), but the level oftreatment in the present study was �4-fold of that in theseprevious experiments. We did prove that the level ofsupplementary feeding applied had a positive effect onfemale body mass during late gestation and on offspringbirth masses for smaller females. Female body mass did,

Table 3. Estimates from linear models (LM) relating offspring birth mass (a) and birth date (b) to experimental manipulation of winterconditions (CO; ‘natural pastures’, and SF’; ‘supplementary feeding’), reproductive manipulation (CO; ‘lack of offspring removal’ and ‘LA’;‘offspring removal’) and initial female body mass. The intercept shows mass for control females. To make the Intercept biologicallymeaningful initial body mass was centered (subtracting the average body mass). Estimated parameters are for a model selected from a pool ofcandidate models (details in Appendix 2 and Fig. 4).

Parameter Lagged effects


(a) Female spring mass (kg)Intercept 84.13 [82.27,85.99]Environmental manipulation (SF) 1.84 [�0.83,4.52] 0.17Reproductive manipulation (LA) 1.46 [�1.13,4.05] 0.26Initial body massa 0.97 [0.77,1.17] B0.01Env. man. (SF)�Reprod. man (LA) �1.70 [�5.50,2.10] 0.37Env. man. (SF)�Initial body massa �0.30 [�0.53,�0.07] 0.01Reprod. man (LA)�Initial body massa �0.06 [�0.29,0.17] 0.60

(adjusted R2�0.78, F�34.39, DF�6,51, p B0.01)

(b) Offspring birth mass (kg)b

Intercept 6.22 [5.86,6.59]Environmental manipulation (SF) �0.20 [�0.70,0.30] 0.43Reproductive manipulation (LA) 0.02 [�0.46,0.51] 0.92Initial body massa 0.03 [0.01,0.05] 0.01Env. man. (SF)�Reprod. man (LA) 0.45 [�0.24,1.14] 0.20

(adjusted R2�0.12, F�2.76, DF�4,50, p�0.04)

(c) Offspring birth date (days)c

Intercept 4.06 [3.63,4.48]Environmental manipulation (SF) �0.18 [�0.75,0.40] 0.54Reproductive manipulation (LA) �0.09 [�0.65,0.47] 0.76Env. man. (SF)�Reprod. man (LA) 0.38 [�0.41,1.18] 0.34

(adjusted R2��0.03, F�0.40, DF�3,51, p�0.75)

aMaternal body mass in January 2007 (i.e. before onset of manipulation).bOne potential outlying observation, i.e. the birth mass of 9.1 kg, was detected, but as its removal did not affect the conclusion drawn fromthis analysis we kept it in the analysis.cBirth date, i.e. the number of days from 1 May, was square root transformed in order to approximate normally distributed residuals.Consequently, the reported estimates in this table are on square root scale.

8

however, increase from early to late winter in the naturalpastures group as well, and this increase in body massduring winter makes this study herd quite different fromthe other experiments (Fig. 5b in Fauchald et al. 2004).Moreover, winter and spring body masses in this herd issubstantially larger compared to most other Fennoscandianherds (Lenvik and Aune 1988, Rødven 2003, Tveraa et al.2003, Fauchald et al. 2004, Bardsen et al. 2008, Bardsenet al. unpubl.). Consequently, the issue of whether thistreatment was realistic with respect to a ‘natural’ Fennos-candian setting is hard to argue for. Nevertheless, the foragesituation that reindeer in Kaamanen experiences representan interesting situation when studying risk sensitive lifehistories as the winter situation for this herd is associatedwith low levels of risk: winter feeding conditions areoverabundant and highly predictable across years. Femalesin all the experimental groups, thus, seem to invest a largeamount of resources into both reproduction and somaticgrowth. This makes this study quite different from ourprevious experiments where later winter feeding conditionshave been highly unpredictable (Tveraa et al. 2003,Fauchald et al. 2004, Bardsen et al. 2008). In essence, thepresent study represents a nice complement to our previousstudies as it improves our knowledge about the cost of

reproduction and reproductive allocation in a low riskenvironment.

Cost of reproduction

Lactation was clearly immediately costly for reindeer asbarren females were larger compared to lactating females inthe autumn, whereas all experimental groups were of equalsize in the summer. The latter result supports earlier findingsthat female reindeer regulate their body mass down to someminimum spring threshold in order to take care of theirnewborns at a time when the chance of starvation is low(Fauchald et al. 2004, Bardsen et al. 2008). Barren femalesinvested more in somatic growth during summer comparedto lactating ones as they gained more in body mass comparedto lactating females. We found no delayed costs ofreproduction as no lagged effects of reproductive manipula-tion was present in the spring of 2008.

The cost of reproduction for large herbivores living innorthern hemisphere is generally, not related to reducedsurvival but rather to reduced future reproduction (Festa-Bianchet et al. 1998, Festa-Bianchet and Jorgenson 1998),and adult survival is high and constant relative to juvenile

65

70

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85

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95

100Control

Fem

ale

sprin

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(a)Supplementary feeding

(b)

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(kg)

(c)

Reproductiv e manipulationControl

Offspring removal

(d)

2

3

4

5

6

60 70 80 90

bir

th d

ate

(d

ays

)

(e) (f)

Initial female body mass (kg)60 70 80 90 100

Figure 4. Female spring body mass (a�b), birth mass (c�d) and birth date (e�f), which is square root transformed, in 2008 as a function ofinitial female body mass (8 January 2007) and experimental group (birth mass; mean�6.27 kg90.67 SD, n�55 and birth date;mean�16.64 days96.08 SD, n�55). This is a visualization of data and models with non-centered initial body mass presented in Table3. The panels divide environmental manipulation: left panel (a, c and e) represents controls whereas right panel (b, d and f) represents thesupplementary feeding group (details in Table 3).

9

survival for these organisms (Gaillard et al. 1998, 2000).Nevertheless, reproductive allocation has a negative effecton maternal body mass for reindeer (Bardsen et al. 2008,this study). Such a cost of reproduction with respect tomaternal autumn body mass can have important effects onother life history traits as well (through correlations withbody mass), e.g.: (1) reproductive success (Cameron et al.1993, Kojola 1993, Fauchald et al. 2004); (2) female age(Reimers et al. 1983, Kojola et al. 1998, Rødven 2003); (3)survival of both juveniles and adults (Tveraa et al. 2003);and (4) social rank (Kojola 1989, Holand et al. 2004,Fauchald et al. 2007). A combination of an extreme winterand low body mass will be fatal even for adult reindeer(Tveraa et al. 2003).

Risk sensitive in the context of the present study combinesthe probability of encountering an extreme winter and theconsequences such winters have on survival and reproductivesuccess. The animals cannot manipulate the probability ofencountering such a winter, but they can buffer the adverseconsequences of such winters by reducing their reproductiveallocation (Adams 2005, Bardsen et al. 2008, this study).Thus, it is important to keep in mind that female reindeer donot prepare for an average winter, but for extreme events thatmight happen from time to time. In sum, the immediate costof lactation found in the present study are in accordance withnumerous observational studies on mammals (Clutton-Brock et al. 1989, Dufour and Sauther 2002) and with thegeneral finding that reproduction is costly: mammals ingeneral (Sand 1996, Festa-Bianchet et al. 1998, Lambin andYoccoz 2001, Lummaa and Clutton-Brock 2002, Tveraaet al. 2003, Tavecchia et al. 2005), birds (Linden and Møller1989, Moreno 1989, Monaghan and Nager 1997) and plants(Obeso 2002).

Reproductive allocation

We found no evidence of a positive immediate effect ofimproved winter conditions on reproductive allocationduring summer, which was measured as an increase inoffspring body mass from early summer to autumn in 2007.Actually, this was not surprising as this is the thirdexperiment on reindeer where no positive effects of winterfeeding on reproductive output has been documented(Fauchald et al. 2004, Bardsen et al. 2008). Nevertheless,we were able to find evidence of a positive effect of improvedwinter on offspring birth mass for smaller females. Thisfinding may indicate that there is an upper body massthreshold, i.e. a regulatory mechanism controlling theamount of resources a mother can give to a fetus, affectingreproductive output in the spring as both smaller and largerfemales produced offspring of similar size in the supple-mentary feeding group. Existence of body mass thresholdsaffecting reproduction has been found previously (reviewedby Gaillard et al. 2000): lower body mass thresholds abovewhich most females reproduce and below which they do nothas been found in e.g. red deer (Albon et al. 1983), moose(Sæther and Haagenrud 1983, Sæther et al. 1996), bighornsheep (Jorgenson et al. 1993) and reindeer (Reimers 1983,

Skogland 1985), whereas an upper threshold where increas-ing mass do not lead to increased reproductive output as hasbeen found previously for reindeer (Lenvik et al. 1988).Moreover, except for the finding that initially small femalesthat received supplementary winter feeding the previous yearwere larger compared to control females we did not find anylagged effects of manipulation in the spring of 2008. Inessence, improved winter feeding conditions lead to in-creased reproductive allocation in the fetus during gestationbut not during the lactation period.

Risk sensitive life histories

In a previous experimental study we concluded that whenreproduction competes with the amount of resourcesavailable for survival during an unpredictable non-breedingseason, individuals adopted a risk sensitive regulation oftheir reproductive allocation (sensu Bardsen et al. 2008).Moreover, Bardsen et al. (2008) argued that for a givendistribution of winter conditions, a risk prone reproductivestrategy involves high reproductive allocation that will resultin high reproductive reward during benign winters but highsurvival cost during harsh winter. A low reproductiveallocation will, on the other hand, result in stable wintersurvival but lower potential reproductive reward, and thisrepresents a risk averse reproductive strategy. These con-trasting reproductive strategies can only be understood inrelation to the expected environmental conditions, i.e. thedistribution of past environmental conditions experiencedby the females. Based on that, Bardsen et al. (2008) arguedthat when benign winter conditions appear over severalyears, individuals should increase their reproductive alloca-tion. This increase in reproductive allocation should happeneven though individuals have to trade allocation inreproduction over their own chance to survive (if a harshwinter do occur) as the amount of autumn body reservesneeded as insurance against winter starvation is loweredunder benign conditions. Similarly, this means that the costof reproduction is lowered when winter conditions areimproved as survival probabilities for both females andoffspring are improved under benign conditions. Thewinter feeding conditions in Kaamanen are superiorcompared to most other Fennoscandian herds so ourfinding of no large delayed, but some immediate, costs ofreproduction and reproductive investments due to im-proved conditions, thus, fits well with theory.

Acknowledgements � The present study was funded by the ResearchCouncil of Norway. We thank Heikki Tormanen, Jukka Siitariand Sari Siitari at the Reindeer Res. Stn of Finnish Game andFisheries Res. Inst., Kaamanen, Finland as well as Inga-BritaMagga and Mika Tervonen, Finnish Reindeer Herding Associa-tion for allowing us to use their study facilities and animals in ourexperiments, and for assisting us in the field at various circum-stances. Various comments from Marius W. Næss, John A.Henden, Marco Festa-Bianchet and Jean-Michel Gaillard greatlyimproved our manuscript. Discussions with Nigel G. Yoccoz, RolfA. Ims, Børge Moe, Jan O. Bustnes, Svein A. Hanssen, Kjell E.

10

Erikstad, Geir H. Systad, Jouko Kumpula, Øystein Holand andKnut H. Røed have been useful in forming the present study.

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Forchhammer, M. C. et al. 2001. Climate and population densityinduce long-term cohort variation in a northern ungulate. � J.Anim. Ecol. 70: 721�729.

Gaillard, J. M. and Yoccoz, N. G. 2003. Temporal variation insurvival of mammals: a case of environmental canalization?� Ecology 84: 3294�3306.

Gaillard, J. M. et al. 2000. Temporal variation in fitnesscomponents and population dynamics of large herbivores.� Annu. Rev. Ecol. Syst. 31: 367�393.

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Hadley, G. L. et al. 2007. Evaluation of reproductive costs forWeddell seals in Erebus Bay, Antarctica. � J. Anim. Ecol. 76:448�458.

Holand, O. et al. 2004. Social rank in female reindeer (Rangifertarandus): effects of body mass, antler size and age. � J. Zool.263: 365�372.

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11

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12

Appendix 1. Test of experimental design

We tested the design and found no statistical significantdifferences between the experimental groups for initialfemale body mass and age (Fig. A1.1). We used a two-way analysis of variance (using the treatment contrast:Venables and Ripley 2002) including both manipulationsand the interaction between them (Table A1.1).

Table A1.1. Estimates from linear models (LM) relating initial female body mass (a) and age (b) to experimental manipulation of winterconditions (CO; ‘natural pastures’, and SF’; ‘supplementary feeding’) and experimental manipulation of lactation (CO; ‘lack of offspringremoval’ and ‘LA’; ‘offspring removal’). The intercept shows estimated values for control females for both manipulations.

Parameter Reproductive investment


(a) Initial body mass (kg)Intercept 77.65 [73.63,81.66]Environmental manipulation (SF) 0.30 [�5.30,5.89] 0.92Reproductive manipulation (LA) 0.19 [�5.41,5.78] 0.95Env. man. (SF)�Reprod. man. (LA) �0.13 [�8.04,7.78] 0.97(adjusted R2��0.05, F�0.01, DF�3,66, p�0.99)

(b) Initial female age (years)Intercept 6.41 [4.95,7.88]Environmental manipulation (SF) 0.42 [�1.62,2.46] 0.68Reproductive manipulation (LA) 0.59 [�1.45,2.63] 0.57Env. man. (SF)�Reprod. man. (LA) �0.66 [�3.51,2.23] 0.65(adjusted R2��0.04, F�0.12, DF�3,66, p�0.95)

70

75

80

85

(a) Female body mass (kg)

Control

Offspring removal

Reproductive manipulation

4

5

6

7

8

9

10

Control Supplementary feeding

(b) Female age (year)

Environmental manipulation (winter conditions)

Mea

n ±

st.

dev.

Figure A1.1. Estimated mean initial female body mass (8 January) and age for the different experimental groups presented with91 SD(bars).

Reference

Venables, W. N. and Ripley, B. D. 2002. Modern appliedstatistics with S. � Springer.

13

Appendix 2. Model selection and the set ofcandidate models

Selecting the models used for inference in the threeanalyses presented was performed within a model selectionframework (Buckland et al. 1997, Anderson et al. 2000,Burnham and Anderson 2002): First, a set of candidatemodels was defined. Defining the set of candidate models isan important but often underemphasized part of anstatistical analysis: ‘models without biological supportshould not be included in the set of candidate models’(Burnham and Anderson 2002). Thus, we included somepredictors in the analyses based on our a priori expectations(see main text for details; Table A2.1�3). Second, in eachanalysis, rescaling and ranking models relative to the valueof the model with the lowest Akaike’s information criterion(AIC) value was performed (Burnham and Anderson 2002:Di denotes this difference for model i ). We, then, selectedthe simplest model (i.e. the model with the fewest degrees offreedom) with a Di 5 1.5.

Table

A2.1

.Th

ere

lative

evid

ence

for

each

candid

ate

LME

model

inTa

ble

1(i

)w

asas

sess

edby

resc

alin

gan

dra

nki

ng

model

sre

lative

toth

eva

lue

of

the

model

wit

hth

elo

wes

tA

kaik

e’s

info

rmat

ion

crit

erio

nva

lue

(Di;

the

model

under

lined

inbold

wer

ese

lect

edan

duse

dfo

rin

fere

nce

inea

chan

alys

isas

its

Di

equal

sze

ro).

The

model

sw

ere

fitted

by

max

imum

like

lihood

(ML)

asth

ere

stri

cted

max

imum

like

lihood

(REM

L)fituse

din

the

Table

1an

d3

are

notre

com

men

ded

when

seve

ralm

odel

sar

eco

mpar

edto

each

oth

er(P

inhei

roan

dB

ates

2000).

Each

pre

dic

tor

incl

uded

ina

model

ism

arke

dw

ith

an‘x

’,w

her

eas

those

mar

ked

wit

ha

‘-‘

isnot

avai

lable

for

that

spec

ific

anal

ysis

.

iEn

viro

nm

enta

lm

anip

ula

tion

aR

epro

duct

ive

man

ipula

tion

aSe

ason

aEn

v.m

anip

.�R

epro

d.

man

ip.a

Env.

man

ip.�

seas

.aR

epro

d.

man

ip.�

seas

.aEn

v.m

anip

.�R

epro

d.

man

ip.�

seas

.a

Initia

lbody

mas

s(I

BM

)R

epro

d.

man

ip.�

IBM

Env.

man

ip.�

IBM

)O

ffsp

ring

sex

(OFS

Env.

man

ip.�

OFS

Rep

rod.

man

ip.�

OFS

DF

Inve

stm

ent

inso

ma

vsre

pro

duct

ion

Di

(a)

Fem

ale

body

mas

s(k

g)1.

xx

xx

xx

xx

xx

xx

x24

3.6

62.

xx

xx

xx

xx

xx

xx

23

1.9

33.

xx

xx

xx

xx

xx

x22

2.2

44.

xx

xx

xx

xx

xx

21

1.9

65.

xx

xx

xx

xx

x20

0.0

06.

xx

xx

xx

xx

19

1.0

4b

7.

xx

xx

xx

x18

119.4

2

(b)

Off

spri

ng

body

mas

s(k

g)c

1.

x�

x�

x�

xx

x�

xx

�10

1.2

72.

x�

x�

x�

xx

x�

x9

0.0

03.

x�

x�

x�

xx

x8

4.8

74.

x�

x�

x�

xx

73.5

65.

x�

x�

x�

x5

13.2

0

aTh

epre

dic

tors

inbold

wer

eke

pt

inal

lm

odel

sbas

edon

our

apri

ori

expec

tati

ons.

bW

ela

ckin

form

atio

non

the

sex

of

the

offsp

ring

for

afe

wfe

mal

es:

(i)

we

do

not

know

ifone

fem

ale

gave

bir

than

d(ii)

one

fem

ale

did

not

give

bir

th.

Since

offsp

ring

sex

was

not

import

ant

we

fitt

edth

ese

lect

edm

odel

todat

aw

her

ew

eal

soin

cluded

thes

eth

ree

indiv

idual

s.cD

ata

from

Mar

chto

May

was

not

incl

uded

inth

ese

anal

yses

asth

efi

rst

gath

erin

gw

ith

all

off

spri

ng

incl

uded

was

inJu

ne.

References

Anderson, D. R. et al. 2000. Null hypothesis testing:problems, prevalence, and an alternative. � J. WildlifeManage. 64: 912�923.

Buckland, S. T. et al. 1997. Model selection: an integralpart of inference. � Biometrics 53: 603�618.

Burnham, K. P. and Anderson, D. R. 2002. Modelselection and multimodel inference: a practical informa-tion-theoretic approach. � Springer.

Pinheiro, J. C. and Bates, D. M. 2000. Mixed effectmodels in S and S-PLUS. � Springer.

14

Table

A2.2

.Th

ere

lative

evid

ence

for

each

candid

ate

LMm

odel

inTa

ble

2(i

)w

asas

sess

edby

resc

alin

gan

dra

nki

ng

model

sre

lative

toth

eva

lue

of

the

model

wit

hth

elo

wes

tA

kaik

e’s

info

rmat

ion

crit

erio

nva

lue

(Di;

the

model

inunder

lined

inbold

wer

ese

lect

edan

duse

dfo

rin

fere

nce

inea

chan

alys

isas

its

Dieq

ual

sze

ro).

Each

pre

dic

tor

incl

uded

ina

model

ism

arke

dw

ith

an‘x

’

iEn

viro

nm

enta

lm

anip

ula

tion

aIn

itia

lbody

mas

s(I

BM

)En

v.m

anip

.�IB

MO

ffsp

ring

sex

(OFS

)En

v.m

anip

.�O

FSD

FR

epro

duct

ive

inve

stm

ent

Di

(a)

Off

spri

ng

bir

thm

ass

(kg)

1.

xx

xx

x7

2.0

62.

xx

xx

60.4

33.

xx

x5

0.0

0b

4.

xx

44.3

55.

x3

17.9

1

(b)

Off

spri

ng

bir

thdat

e(d

ays)

c

1.

xx

xx

x7

3.7

12.

xx

xx

61.7

13.

xx

x5

1.5

34.

xx

40.0

0b

5.

x3

5.1

0

aThe

pre

dic

tor

inbold

was

kept

inal

lm

odel

sbas

edon

our

apri

ori

expec

tati

ons.

bW

ela

ckin

form

atio

non

the

sex

of

the

off

spri

ng

for

afe

wfe

mal

es(T

able

A2.1

).Si

nce

offsp

ring

sex

was

not

import

ant

we

fitt

edth

ese

lect

edm

odel

todat

aw

her

ew

eal

soin

cluded

thes

ein

div

idual

s.cB

irth

dat

e,i.

e.th

enum

ber

of

day

sfr

om

1M

ay,

was

squar

ero

ot

tran

sform

edin

ord

erto

appro

xim

ate

anorm

aldis

trib

uti

on

for

the

resi

dual

s.

15

Table

A2.3.

The

rela

tive

evid

ence

for

each

candid

ate

LMm

odel

inTa

ble

3(i

)w

asas

sess

edby

resc

alin

gan

dra

nki

ng

model

sre

lative

toth

eva

lue

ofth

em

odel

wit

hth

elo

wes

tA

kaik

e’s

info

rmat

ion

crit

erio

nva

lue

(Di;

the

model

inunder

lined

inbold

wer

ese

lect

edan

duse

dfo

rin

fere

nce

inea

chan

alys

isas

its

Dieq

ual

sze

ro).

Each

pre

dic

tor

incl

uded

ina

model

ism

arke

dw

ith

an‘x

’

iEn

viro

nm

enta

lm

anip

ula

tion

aR

epro

duct

ive

man

ipula

tion

aEn

v.m

anip

�R

epro

d.

man

ipa

Init

ial

body

mas

s(I

BM

)R

epro

d.

man

ip.�

IBM

Env.

man

ip.�

IBM

Env.

man

ip�

Rep

rod.

man

ip�

IBM

Off

spri

ng

sex

(OFS

)R

epro

d.

man

ip.�

OFS

Env.

man

ip.�

OFS

DF

Lagg

edef

fect

s

Di

(a)

Fem

ale

spri

ng

mas

s(k

g)1.

xx

xx

xx

xx

xx

12

5.3

02.

xx

xx

xx

xx

x11

4.1

83.

xx

xx

xx

xx

10

3.3

94.

xx

xx

xx

x9

1.9

45.

xx

xx

xx

80.0

0b

6.

xx

xx

x7

4.5

17.

xx

xx

62.6

08.

xx

x5

84.2

9

(b)

Offsp

ring

bir

thm

ass

(kg)

1.

xx

xx

xx

xx

xx

12

9.8

52.

xx

xx

xx

xx

x11

9.0

83.

xx

xx

xx

xx

10

7.3

14.

xx

xx

xx

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5.4

25.

xx

xx

xx

83.4

76.

xx

xx

x7

1.8

27.

xx

xx

60.0

0b

8.

xx

x5

5.4

2

(c)

Off

spri

ng

bir

thdat

e(d

ays)

c

1.

xx

xx

xx

xx

xx

12

7.6

12.

xx

xx

xx

xx

x11

5.8

03.

xx

xx

xx

xx

10

3.8

94.

xx

xx

xx

x9

4.0

45.

xx

xx

xx

84.9

86.

xx

xx

x7

3.2

17.

xx

xx

61.2

78.

xx

x5

0.0

0b

aThe

pre

dic

tor

inbold

was

kept

inal

lm

odel

sbas

edon

our

apri

ori

expec

tati

ons.

bW

ela

ckin

form

atio

non

the

sex

of

the

off

spri

ng

for

afe

wfe

mal

es(T

able

A2.1

).Si

nce

off

spri

ng

sex

was

not

import

ant

we

fitt

edth

ese

lect

edm

odel

todat

aw

her

ew

eal

soin

cluded

thes

ein

div

idual

s.cB

irth

dat

e,i.e.

the

num

ber

of

day

sfr

om

1M

ay,

was

squar

ero

ot

tran

sform

edin

ord

erto

appro

xim

ate

anorm

aldis

trib

uti

on

for

the

resi

dual

s.

16

ERRATA: author suggested corrections for the proof P1, title. ‘(…) costs of lactation (…)’ should read ‘(…) cost of lactation (…)’ as we only

documented one cost of lactation: the effect of ‘LA’ on female bm in the autumn of 2007. P1, addresses. Mauri Nieminen is not employed at NINA. His affiliation is solely at ‘Finnish

Game and Fisheries Research Inst., Reindeer Research Station, FI-99910 Kaamanen, Finland’.

P1, Abstract. ‘In contrast, offspring removal did have a positive effect on summer body mass

development as females in this group were larger in the autumn body mass relative to control females’ should read ‘In contrast, offspring removal did have a positive effect on summer body mass development as females in this group were larger in the autumn relative to control females’.

P1, 1st paragraph (left column), line 7 from below. ‘(…) reproductive stages but most studies

have (…)’ should read ‘(…) reproductive stages, but most studies have (…)’. P2, Figure 1. The frame around one of the boxes is missing: The first ‘SF’ box should have a

similar frame as the other ‘SF’ box. P3, 2nd paragraph (right column), line 27 from above. ‘One female in the offspring removal

groups had (…)’ should read ‘One female in the offspring removal group had (…)’. P3, 2nd paragraph (right column), line 15 from below. ‘(…) in October 2008 (…)’ should read

‘(…) in October 2007 (…)’. P3, 1st paragraph (right column), line 19-20 from above. ‘(…) (1 = 1 May, 2 = 2 May, …, k =

k days from 1 May) (…)’ should read ‘(…) (1 = 1 May) (…)’. P4, 2nd paragraph (left column), line 10-14 from above. ‘For females, experimental

manipulation of environment (control and supplementary feeding) and reproduction (control and lactation), initial female body mass (January prior to manipulation) and season (March, April, June and October) were applied as fixed effects (Fig. 1), (…)’ should read ‘‘For females, experimental manipulation of environment (control and supplementary feeding) and reproduction (control and lactation), initial female body mass (January prior to manipulation), season (March, April, June and October) and offspring sex (female and male) were applied as fixed effects (Fig. 1), (…)’.

P4, 3rd paragraph (left column), line 16-15 from below. ‘From this pool of models we selected

the model with the lowest Akaike’s information criterion (AIC) value, (…)’ should read ‘From this pool of models we selected the most parsimonious model as assessed by the Akaike’s information criterion (AIC) (…)’.

P9, 1st paragraph (left column), line 9 from below. ‘(…) low levels of risk: winter feeding

conditions are overabundant (…)’ should read ‘(…) low levels of risk: winter forage is overabundant (…)’.

P10, 2nd paragraph (right column), line 1 from below. ‘(…) Bustnes, Svein A. Hanssen (…)’

should read ‘(…) Bustnes, Sveinn A. Hanssen (…)’.

P13, 1st paragraph (left column), line 1 from above. ‘(…) no statistical significant (…)’ should read ‘(…) no statistical significantly (…)’.

P13, Table A1.1, heading. ‘Reproductive investment’ should read ‘Design conditions’. P14-16, Table A2.1-3, table text. ‘(…) Δi equals zero’ should read ‘(…) Δi ≥ 1.5’. P14-15, Table A2.1-2, label for last column to the right. ‘investment’ should read ‘allocation’. P1-16, ‘search and replace’: non-consistency in the text. 1. We have used ‘vs’, ‘vs.’ and ‘versus’ non-consistently throughout the manuscript. 2. In the proof ‘a priori [in normal text]’ have been used whereas ‘a priori [in italics]’ is used

consistently in the literature. 3. The appendices are in the main text referred to as both ‘Appendix A1’ and ‘Appendix A2’ or

as ‘Appendix 1’ and ‘Appendix 2’. We do not have any preferences, but we think that this should be consistent. Please do note that we started the labelling of all figures/tables in the appendixes with ‘A’. Figure 1 in Appendix 1 is for example labelled as ‘Figure A1.1’.

PAPER 3

Observational evidence of a risk sensitive

reproductive allocation in a long-

lived mammal

Bårdsen, B.-J., T. Tveraa, P. Fauchald & K. Langeland

Manuscript

Running head: Risk sensitive reproductive allocation

Title: Observational evidence of a risk sensitive reproductive allocation in a long-lived mammal

List of authors: Bård-Jørgen Bårdsen a ,b ,1, Torkild Tveraa a,2, Per Fauchald a,b,3 & Knut Langeland a,b,4

a Norwegian Institute for Nature Research (NINA), Division of Arctic Ecology, Polar Environmental Centre, N-9296

Tromsø, Norway.

b University of Tromsø (UIT), Department of Biology, N-9037 Tromsø, Norway.

1 E-mail: [email protected] (author for correspondence)

2 [email protected]

3 [email protected]

4 [email protected]

mailto:[email protected]




Risk sensitive reproductive allocation 2

Abstract: In a previous study we found that organisms can adopt a risk sensitive reproductive

allocation when summer reproductive allocation competes with survival in the coming winter

(Bårdsen et al. 2008). This trade off is present through autumn female body mass, which acts as an

insurance against unpredictable winter environmental conditions. In the present study we tested

this hypothesis on female reindeer in a population that has experienced a time-period of dramatic

strong increase in abundance. Environmental conditions during winter were at the same time fairly

stable (with the exception of one year). We conclude that the increased population abundance

(perhaps in interaction with winter environmental conditions) represented a worsening of winter

environmental conditions as both autumn offspring and spring female body mass decreased

during the course of the study. Moreover, we found that the cost of reproduction was related to

environmental conditions as: (1) autumn body mass was larger for barren than for lactating

females, and this difference was temporally highly variable; (2) lactating females produced smaller

offspring than barren ones in the following year; and (3), reproductive output (offspring size)

decreased over time. We also found evidence of an individual quality difference as lactating

females had a higher reproductive success in the following year. In sum, a worsening of winter

conditions lead to (1) decreased reproductive output, (2) lowered autumn body mass for lactating

and (3) increased body mass for barren females. Since female reduce their reproductive allocation

as winter conditions becomes more unpredictable we conclude that reindeer have adopted a risk

sensitive reproductive allocation.

Key words: cost of reproduction; environmental stochasticity; life history; phenotypic plasticity;

Rangifer tarandus.


INTRODUCTION

A central issue in life-history theory is how individuals balance reproductive investments against

their own chances to survive and reproduce in the future (Roff 1992; Stearns 1992). This trade-off

between current reproduction and future survival is commonly referred to as the cost of

reproduction (sensu Williams 1966), and this has been documented in a wide range of taxa:

mammals (Clutton-Brock et al. 1989; Festa-Bianchet et al. 1998; Gittleman and Thompson 1988;

Lambin and Yoccoz 2001; Sand 1996; Tavecchia et al. 2005) including humans Homo sapiens and

other primates (Anderson 1983; Bronson 1995; Dufour and Sauther 2002; Ellison 2003; Lummaa

and Clutton-Brock 2002), birds (Lindén and Møller 1989; Monaghan and Nager 1997; Moreno

1989; Zammuto 1986) and plants (Obeso 2002).

Long-lived organisms favour own survival over reproduction as reproductive output and

juvenile survival are more variable than adult survival (Gaillard et al. 2000; Gaillard and Yoccoz

2003). However, the balance between reproduction and survival should depend on environmental

conditions affecting the two traits (Bårdsen et al. 2008; Forchhammer et al. 2001; Gaillard and

Yoccoz 2003; Sæther 1997). For long-lived species with several breeding attempts, such as

northern large terrestrial herbivores, reproduction generally takes place during the favourable

season (summer), whereas survival is particularly constrained in the unfavourable season (winter:

Sæther 1997). In a variable environment where the amount of resources needed for survival during

winter are difficult to predict, long-lived species should adopt a risk sensitive reproductive strategy

(Bårdsen et al. 2008). Consequently, body size or mass (a proxy for condition or reserves) is an

important trait affecting both survival and reproduction, and hence the cost of reproduction [e.g.

humans (Lummaa and Clutton-Brock 2002), terrestrial large herbivores (Sæther 1997), birds

(Hanssen et al. 2005; Parker and Holm 1990), fish (Hutchings 1994; van den Berghe 1992) and

reptiles (Radder 2006; Shine 2005)]. Body mass, thus, acts as an important state variable (e.g.


Houston and McNamara 1999), which in this case is a currency that can be traded for

reproduction or survival.

In northern and clearly seasonal environments, late winter conditions have profound effects on

survival and reproduction (Coulson et al. 2001; Coulson et al. 2000; DelGiudice et al. 2002;

Patterson and Messier 2000). Autumn body mass, which represents an insurance against winter

starvation is then traded against the resources a female invest in her offspring during summer

(Bårdsen et al. 2008; Clutton-Brock et al. 1996; Fauchald et al. 2004; Reimers 1972; Skogland 1985;

Tveraa et al. 2003). Consequently, in a given summer a female have to choose how much resource

to invest in somatic growth versus reproduction. If a female invest too much in reproduction this

will lead to a lost opportunity for an increased autumn body mass (Bårdsen et al. 2008), and this

will ultimately lower her chance for survival in harsh winters (Tveraa et al. 2003). Thus, the

optimal reproductive strategy, which is defined by the amount of resources to invest in

reproduction relative to somatic growth, will depend on the expected winter environmental

conditions. How individuals optimize this trade-off is related to their body condition, i.e. their

state, and the degree of risk imposed by the environment: an individual has no way of predicting

the future so it has to trade somatic growth against reproductive allocation during summer based

on an ‘estimated’ distribution of winter conditions (Bårdsen et al. 2008).

A changed distribution in winter environmental conditions can, thus, have important

consequences for both reproductive output and survival. Individuals experiencing stable and

benign winter conditions can afford a low autumn body mass and might therefore increase their

fecundity by increased reproductive allocation. On the other hand, animals experiencing harsh and

variable winter conditions should maximize their autumn body mass and should therefore be

limited by a relatively low fecundity and reproductive allocation. Accordingly, northern large

herbivores might have adopted a risk sensitive reproductive allocation in the sense that they adjust

their reproductive allocation during summer according to the risk of starvation the following


winter (see Bårdsen et al. 2008 and references therein). Consequently, individuals can play different

strategies where a risk prone reproductive strategy involves high reproductive allocation that will

result in high reproductive reward during benign conditions but high survival cost during harsh

conditions. A low reproductive allocation will, on the other hand, result in high winter survival but

lower potential reproductive reward. Consequently, this represents a risk averse reproductive

strategy. Such an asymmetric response in the costs and benefits relative to environmental

harshness indicates that long-lived organisms should be on the risk averse side of the risk prone-risk

averse continuum (Bårdsen et al. 2008).

Several experimental studies on female semi-domestic reindeer (Rangifer tarandus) have proved that

reindeer make strategic decisions during summer and that they pay a delayed cost of reproduction

during late winter. First, Tveraa et al. (2003) found that especially harsh winter conditions can

greatly reduce adult survival and reproductive success the following spring and summer. Second,

when late winter feeding conditions are improved adult females increase their late winter body

mass relative to early winter body mass (Fauchald et al. 2004). This gain in body mass is, however,

rapidly lost during the calving season as the above difference in body mass are not present in the

summer (Bårdsen et al. 2008; Fauchald et al. 2004). It has, thus, been concluded that female

reindeer regulate their body mass down to some minimum threshold during spring in order to take

care of their newborns when the risk of starvation is low (Bårdsen et al. 2008; Fauchald et al.

2004). Third, Bårdsen et al. (2008) found that female reindeer have adopted a risk sensitive

reproductive allocation: they found an asymmetric response to improved (no response) vs. reduced

winter conditions where the latter resulted in a prompt reduction in reproductive allocation the

following summer. In essence, additional winter body mass acts primarily as an insurance against

periods of winter starvation, which means that there is a dynamic relationship between summer

and winter as the importance of body mass as a state variable varies across seasons.


We use empirical data from a reindeer herding district in Finnmark, Norway to test predictions on

risk sensitive reproductive allocation in relation to body mass development during summer and

winter (S1). Reindeer abundance drastically increased over and peaked at a historical high-level in

2005 (Fig. 1a), whereas climatic conditions have been relatively stable, with the exception of one

year during the period in which we have detailed individual-data (Fig. 1b-c). Negative interactions

between population density and late winter weather conditions have been documented previously

(e.g. Coulson et al. 2001; Coulson et al. 2000; Grenfell et al. 1998). Consequently, we will argue

that the recent increased abundance, leading to increased competition over resources, had a drastic

effect on the reindeer’s perception of the environment they inhabit. This should again have

changed the cost of reproduction and the optimal balance between how many resources female

reindeer should invest in reproduction relative to somatic growth during summer in a risk sensitive

manner. This is empirically supported as (1) autumn female body mass was unaffected by

increased reindeer abundance, whereas (2) reproductive allocation decreased when reindeer

abundance increased (Fig. 1d-f).

Based on this we predicted that: (1) If female reindeer invest in reproduction during

summer we expected the summer gain in body mass to be higher for barren vs. lactating females,

and that the difference for barren and lactating females to be sensitive to past environmental

conditions. (2) We also expected smaller lactating females to loose less body mass in winter

compared to barren ones due to a quality difference across the two groups. Moreover, the loss of

body mass should be negatively related to population density and winter conditions. (3) If

reproduction is costly we expected summer gain in body mass for offspring to be lower for

females that raised offspring last year. This response, which measure reproductive allocation,

should also be sensitive to past environmental conditions. (4) If reproduction is costly we also

expected that only individuals of superior quality can afford to reproduce where reproductive

success measure another component of reproductive allocation. Thus, reproductive success, i.e.


the probability of having a calf, was predicted to be positively related to maternal body mass and

previous year reproductive status.

MATERIAL AND METHODS

Study population and study area

The present study was conducted on semi-domestic reindeer in Finnmark, Norway (Fig. 1-2). The

study herds (Njarga and Mieron) is most of the time free-ranging. Both herds utilize the same

winter pastures where they are kept together through the winter, but they utilize different summer

pastures. None of the herds was given supplementary feeding. The winter pastures is situated 4-

500 m above sea level (a.s.l.), and this area is characterized by stable and continental winter

conditions (Tveraa et al. 2007). The herds are separated in April and they are then herded ~170

km to their respective summer pastures at the coast. The Njarga herd arrives at their summer

pasture area about 2 weeks later than the Mieron herd as females in this herd give birth during the

migration and not on the summer pastures (Fig. 2). The herds occupy neighbouring areas at the

coast, and the summer pastures consist of rugged mountainous terrain with peaks reaching >1000

m a.s.l. Mixing between herds is practically non-existent as all animals have owner specific

earmarks (if animal are mixed with neighbouring the owner will recognize them and collected by

later on) and as the summer pasture areas are separated by fences and natural barriers such as e.g.

fjords (Fig. 2). During the autumn migration, on the way back to the winter pastures, the two

herds are again mixed and the annual migration cycle is ended.

Study protocol

A random selection of fifty prime-aged female (≥1.5 year) from each herd was individually marked

in April 2002. Since then we have followed the lineages formed by these individuals: i.e. initially


marked females, their offspring, their offspring’s offspring and so on. We record individual body

mass and presence (‘present’ or ‘absent’) in the spring (23rd, 5th, 5th, 4th, 17th, 16th and 28th of April in

2002-2008) and in the autumn (29th, 29th and 30th of October, 3rd of November, 31st of October,

and 11th of November in 2002-2007). Body mass was recorded to the nearest 0.2 kg using an

electronic balance (Avery Berkel, Birmingham, UK). Multiple observations of females with a calf

at foot were used to identify mother-calf relationships, i.e. whether a female was lactating or barren

(see also Bårdsen et al. 2008). This design opens up for the possibility to quantify the relative effect

of winter and summer conditions on individual body mass and reproduction. The dataset contains

the following variables:

Year.-- A factor variable with each year from 2002-2008 acting as levels.

Herd.-- A factor variable with the name of each herd (‘Mieron’ & ‘Njarga’) as levels.

Previous female autumn body mass.-- Female body mass in late October or early November the year

before.

Female spring body mass.-- Female body mass in April.

Reproductive status.-- A variable that either acts as a binary variable (‘0’ & ‘1’) or as a factor variable

(‘negative’ & ‘positive’). Barren females, i.e. individuals registered without a calf, was labelled

‘0’ (binary) or ‘negative’ (factor), whereas lactating females was labelled ‘1’ (binary) or ‘positive’

(factor). This variable was measured in June and September.

Female autumn body mass.-- Female body mass in late October or early November.

Offspring autumn body mass.-- Offspring body mass late October or early November.

Previous reproductive status.-- This variable is similar to ‘reproductive status’ the preceding year.

Age.-- A group of adult females (> 1 year) were included when the study was initiated. In a recent

study from the same study region, we found that age and body mass was highly correlated for

young (≤4 year) reindeer, but not for prime-aged individuals (5-13 year: Bårdsen et al. in

press). This finding is in accordance with Lenvik et al’s (1988) studies well. They found that

body mass was a more important predictor of reproduction than age within the prime-aged


segment. Thus we felt confident that our inability to correct for age did not affect our results

and conclusions (see S1 for details).


An overview of the statistical analyses

Our predictions, which for all analyses of body mass focus on body mass development from one

point in time to another, can statistically be tested by the following comparisons (S1): (1) Autumn

female body mass as a function of spring body mass and reproductive status (Summer body mass

development). (2) Spring female body mass as a function of previous autumn body mass and

previous reproductive status (Winter body mass development). (3) Autumn offspring body mass as a

function of spring maternal body mass and previous reproductive status (Offspring summer body mass

development). (4) Reproductive success, i.e. probability of producing a calf, as a function of spring

maternal body mass and previous reproductive status. (5) Reproductive success as a function of

maternal body mass the previous autumn and previous reproductive status (analysis 4 and 5 are

hereafter termed Reproduction). Covariates were included and excluded within the ‘paradigm’ of

model selection (S1). Statistical analyses were carried out in R (R Development Core Team 2007),

All tests were two-tailed and the null-hypothesis was rejected at an α-level of 0.05.

Body mass

Linear models, using the lm function in R, were used to analyze the effect of the predictors on

body mass of both females and offspring. Our aim was to assess the relative importance of the

cost of reproduction on body mass development across the summer versus winter season. Thus, it

is important to make comparisons between initial body mass (centred in all analyses; subtracting

the average value), i.e. spring or previous autumn condition, across reproductive status. Our study

is, thus, based on planned comparisons, and the predictions can then be tested statistically by

estimating the three key parameters (S1; Fig. S1.1): (1) the main effect of reproductive status, or


previous reproductive status; (2) the main effect of initial body mass; and (3) the two-way

interaction between them. This will provide us with an estimate of the mean difference in body

mass between the lactating and barren group at a constant initial body mass, and how the

relationship between body mass and initial body mass is different for lactating and barren females.

Consequently, we started with the full model containing all the above predictors and interactions

based on a priori expectations. From this model, we formed a pool of candidate models where all

covariates and interactions were removed sequentially, where we selected the model with the

lowest second-order Akaike’s Information Criterion (AICc) value (see S2). As this study consists of

planned comparisons we used the treatment contrast comparing each level of a factor to its baseline

level, and Wald statistics to test if contrasts were significantly different from zero.

Reproduction

Generalized linear models, applied using the glm function in R, with a binary response variable (0 =

‘absent’, 1 = ‘present’), using a logit link function and a binomial distribution, were applied

similarly as in the analyses of body mass in order to quantify female reproductive success (i.e. the

probability that a female had a calf). We adopted the same model selection procedure as in the

analyses of body mass (S3).

Mixed-models – an alternative statistical approach

It can be argued that linear mixed-effect models (Pinheiro and Bates 2000: Body mass) and

generalized linear mixed-effect models (Venables and Ripley 2002: Reproduction), using individual as

a random effect, represent more correct statistical approaches. Estimating statistical significance

and model selection are, however, not straightforward for mixed models (e.g. Pinheiro and Bates

2000; Wood 2006). Consequently, we did not apply this approach, but we fitted the mixed-model

version of the selected model in each analysis and that did not change results notably.


RESULTS

Body mass

Summer body mass development

Initially smaller females gained more body mass summer in than larger females (main effect of

spring body mass; 0.531 kg), and as the reproductive status (RS) × spring body mass interaction

was small and insignificant initial body mass was of equal importance for barren and lactating

females (Table 1a & Fig. 3a). Lactating females was, however, in 2002 on average >4 kg smaller

compared to barren ones (main effect of reproductive status; Table 1a & Fig. 3b). Moreover, the

difference between barren and lactating females were larger in all the following years (negative year

× RS interactions; Table 1a) except for 2007. This interaction was, however, only statistically

significant in 2006; lactating females was now on average 9.63 kg smaller than barren females

(Table 1a). The year-effect on female autumn body mass was positive in all years, which means

that there has been a general upward trend in body mass for barren females (main effect of year;

Table 1a). Finally, females in the Njarga herd gained more in body mass over the summer

compared to females in Mieron (main effect of herd; Table 1a). This may indicate that summer

feeding conditions might be better for Njarga compared to Mieron. To summarize, female

reindeer pay a considerable cost of reproduction during summer, and this cost was temporally

highly-variable.

Winter body mass development

Initially smaller and larger females followed a similar pattern of winter body mass development

[main effect of previous autumn body mass; 1.162 kg (Table 1b & Fig. 3c)]. The relationship

between autumn and spring body mass was, however, weaker for lactating than barren females

[previous reproductive success (PRS) × previous autumn body mass interaction; -0.195 kg (Table

1b)]. This indicates that smaller lactating females had a more positive winter body mass


development compared to barren ones (Fig. 3c). For 2007, however, a negative year and previous

autumn body mass interaction occurred; the importance of initial body mass was, thus, of less

importance in this year. There was a small and negative, but not statistical significant, main effect

of PRS on spring female body mass, and this shows that the difference between lactating and

barren females was small in 2003 (Table 1b & Fig. 3d). However, a statistically significant and

positive year × PRS interaction was evident for 2007 (Table 1b). In this year, lactating females

were on average 2.35 kg larger than barren ones. Consequently, in some years barren females were

on average smaller than lactating ones (even though not statistically significant), while in other

years lactating females was on average larger than barren ones. Interestingly, the year effect on

female spring body mass was negative and decreasing through time, which means that there was a

downward trend in body mass for barren females (Table 1b). This trend is also evident for

lactating females, even though they have not been equally affected by this downward temporal

trend in spring body mass (positive year × PRS interaction; Table 1b). Finally, females in the

Njarga herd was on average smaller compared to females in Mieron [main effect of herd; -2.347 kg

(Table 1b)], indicating that Njarga females afforded to loose more body mass compared to Mieron

females. Moreover, the relationship between autumn and spring body mass was weaker in Njarga

compared to Mieron. To summarize, there was no indications of lactating females loosing more

body reserves compared to barren ones during winter. In fact, in some years lactating females

increased in body mass compared to barren females. Perhaps even more importantly, autumn

body mass was a weaker predictor for spring body mass for lactating compared to barren females.

Moreover, both the difference between barren and lactating females and the predicted relationship

between autumn and spring body mass was temporally variable.

Offspring body mass development

Initially smaller females produced smaller offspring than larger females (main effect of maternal

spring body mass; 0.476 kg), and as the PRS × spring body mass interaction was small and

insignificant spring body mass was of equal importance for females being barren and lactating in


the previous year (Table 1c & Fig. 3e). This also means that even though smaller females produced

larger offspring in an absolute sense, smaller females invested proportionally more in their

offspring. Surprisingly, we found that previously barren females produced significantly larger

offspring compared to previously lactating females [main effect of PRS; -2.450 kg (Table 1c)].

Moreover, we found a large temporal variation in offspring body mass as 2005 and 2006 were

statistical significantly different from 2003 (main effect of year; Table 1c). To summarize, a lagged

cost of reproduction with respect to offspring body mass was evident as offspring body mass was

substantially lower for females that were lactating the previous years compared to those who were

barren. Maternal spring body mass was an important predictor for offspring body mass, which

were temporally highly-variable.

Reproduction

Initially larger females had a higher probability of producing an offspring than smaller females

when previous maternal autumn body mass was as used a predictor (main effect of initial body

mass; 0.069 on logit scale), but not when maternal spring body mass was used as a predictor (Table

2 & Fig. 4). Thus, previous autumn body mass, i.e. before winter had taken its toll, was a poorer

predictor of reproductive success than spring body mass even though the latter relationship nearly

reached statistical significance. Moreover, the effect of initial body mass was similar for females

that were lactating the previous year compared to barren ones as the PRS × initial body mass

interaction was small and insignificant in both analyses (Table 2). Females that successfully

reproduced the previous year were more likely to reproduce again compared to females who were

barren when previous maternal autumn body mass was used as a predictor [main effect of PRS;

0.774 (Table 2b)]. This was not the case in the analysis including maternal spring body mass as a

predictor even though it was nearly statistical significant (Table 2a). Moreover, reproduction

showed a high temporal variation in both analyses, and this temporal variability was fairly similar


across the analyses (Table 2). In sum, females that produced an offspring the year before tended to

have a higher chance of reproducing, and reproductive success were temporally highly-variable.

DISCUSSION

The present study demonstrates that female reindeer have adopted a risk sensitive reproductive

allocation strategy because: (1) We found a considerable cost of reproduction with respect to

autumn body mass; barren females gained significantly less body mass during summer compared

to lactating ones. Interestingly, the difference between barren and lactating females was largest the

summer after the peak in reindeer abundance. Female reindeer, thus, promptly increased their

allocation in somatic growth following a period of dramatic increase in resource competition. (2)

The difference for barren vs. lactating females was smaller in the analysis of spring body mass, but

this trend was temporally variable to such an extent that lactating females had a higher spring body

mass compared to barren ones in some years. A negative interaction between reproductive status

and previous autumn body mass did, however, indicate that spring body mass was larger for

initially smaller lactating than for barren females. (3) Females that reproduced the year before

invested fewer resources in reproduction. Moreover, maternal spring body mass was an important

predictor of offspring body mass; larger females, thus, produced larger offspring relative to smaller

females, but smaller females invested proportionally more in their offspring. (4) Maternal spring

body mass was a significant predictor of reproductive success. When previous maternal autumn

body mass was a predictor, females that lactated the previous year had a significantly higher

reproduction compared to barren ones, which indicates that individual qualities are important.

Reproduction and, thus reproductive allocation, was also sensitive to environmental conditions as

both herd and year was important predictors in the analyses.


Autumn body mass was substantially lower for lactating than for barren females, and in some years

this difference was considerably larger compared to others. Interestingly, we found the largest

difference between barren and lactating females (9.6 kg) in the autumn 2006 (the year after the

peaked in abundance). The upward temporal trend in autumn body mass for barren females

showed that density did not limit the ability for females to gain mass during summer. This is

further empirically supported by the fact that the largest average autumn female body mass

occurred after the peak in reindeer abundance and just after the winter with abnormally high levels

of precipitation (Fig. 1d). Consequently, late winter conditions, defined by both density and

weather (e.g. Coulson et al. 2001), affected how much a female should invest in somatic growth vs.

reproduction. Further, a lowered reproductive allocation was also evident from the lowered

offspring body mass and proportion of females breeding over time (Fig. 1d,f). This trade-off

between allocation in growth vs. reproduction, which occurs in summer, has been found

previously for large herbivores (e.g. Clutton-Brock et al. 1996; Reimers 1972; Skogland 1985), and

the increased allocation in somatic growth over reproduction following a harsh winter is predicted

for a risk averse reproductive strategy (Bårdsen et al. 2008). If we measure the cost of reproduction

as a lost opportunity for summer gain proportional to spring body mass, this cost was considerable

for initially smaller relative to larger females. Moreover, smaller females gained more body mass

over the summer than larger ones. In essence, we documented a large cost of reproduction with

respect to autumn body mass, and this cost was related to past winter conditions. This finding can

be explained by the fact that reindeer have adopted a risk averse reproductive allocation strategy.

For spring body mass we found that individuals were substantially larger in 2003 compared to all

other years. We interpret this decrease in body mass to be an effect of increasing population

abundance acting in concert with harsh winter weather conditions. This is in accordance with

previous studies that have documented that late winter conditions have profound effects on

survival and reproduction for temperate large herbivores (e.g. Coulson et al. 2001; Coulson et al.


2000; DelGiudice et al. 2002; Patterson and Messier 2000; Tveraa et al. 2003). Second, the

difference between lactating and barren females showed a high temporal variation. In fact, no

significant difference between lactating and barren females was found in most years. Nevertheless,

lactating females did have the highest spring body mass in 2007. This was perhaps due to an

interaction between density, which was stable from 2005, and climate as this year had abnormally

high winter precipitation levels (Fig. 1c). This might have increased resource competition during a

particularly harsh winter. Third, we did find a more positive relationship between previous autumn

and spring body mass for barren compared to lactating females, indicating that smaller lactating

outperformed smaller barren females. This effect was, thus, the opposite of that found in the

previous analysis (van Noordwijk and de Jong 1986 show how positive relationship between two

traits subject to trade-offs might occur). Autumn body mass may, thus, act differently for barren

and lactating females due to a quality difference between them. Social dominance, may, be a

mechanism explaining this relationship (Kojola 1989). However, female reindeer regulate their

body mass down to some minimum threshold during spring when the risk of starvation is low

(Bårdsen et al. 2008; Fauchald et al. 2004), which may also explain why we did not find a clear cost

of reproduction on female spring body mass. In conclusion, the difference in spring body mass for

lactating and barren females were not clearly present as lactating females can outperform barren

ones. In contrast to the previous analysis, we found a strong negative trend in spring body mass

related to an interaction between density dependence and winter conditions.

Maternal spring body mass was a positive predictor of offspring autumn body mass. Surprisingly,

we documented a lagged cost of reproduction on offspring body mass: females that were lactating

the previous year produced calves that were on average ~2.5 kg, i.e. ~6%, smaller compared to

barren ones. In the analysis of offspring body mass, as in the analysis of maternal spring body

mass, 2003 was a particularly favourable year as offspring body mass was lower for all following

years (Fig. 1e). This, in combination with the previous analyses, shows that the cost of


reproduction has two components; (1) a direct cost related to adult survival manifested as a lost

opportunity for summer gain in body mass, and (2) a lagged cost related to reproductive success

manifested as a reduction in offspring body mass in the next breeding season.

Previous studies on reindeer have revealed that body mass as a state variable have different

interpretation depending on seasons: (1) Autumn body mass represents an insurance against

winter severity (Bårdsen et al. 2008) and (2) female reindeer regulate their body mass down to a

threshold value during the spring in order to take care of their newborns (Fauchald et al. 2004).

Based on this we modelled reproductive success with two sets of initial female body masses as

predictors. In both analyses, reproduction was positive related to previous reproductive success

even though it was only barely statistically significant in the analysis of previous autumn body

mass. The analysis of reproduction can, thus, be said to be non-consistent with the analysis of

offspring body mass. We interpret the positive effect of successful reproduction the year before

was as evidence of individual differences in quality. Alternatively, this may reflect that females are

reproducing more or less continuously after reaching maturation, but this is not likely as the

proportion of females reproducing each year was highly variable (range: 0.6-0.9). Maternal body

mass was, then, a positive predictor of reproduction showing that larger females had a higher

reproductive success compared to smaller ones. The weaker effect of previous autumn body mass

on reproductive success may be explained by the fact that this represents another ‘currency’

compared to spring mass, which reflects individual states in the beginning of the breeding season.

In conclusion, we found evidence of individual variation in quality as we documented a lagged

positive effect of previous year’s reproductive success

We demonstrate that female reindeer have adopted a risk sensitive reproductive strategy where

they are on the risk averse side of the risk prone-risk averse continuum. We found that a dynamic

interplay between the favourable summer season, which is a period of resources abundance, and


the severe winter season, which is a period where population density interacts with environmental

conditions. The degree of winter severity is, thus, characterized by an interaction between winter

weather, e.g. precipitation and icing events (e.g. Solberg et al. 2001), and density dependent

competition over already scarce resources. We argue that summers are truly favourable as autumn

body mass for barren females increased over time, which means that density during summer was

not a limiting factor. Moreover, we found a substantial cost of reproduction with respect to a lost

opportunity for summer gain in body mass, and we also found a decreased allocation in

reproduction under high density as both offspring body mass and the proportions of females

breeding was lowered as reindeer abundance increased (Fig. 1). Individuals’, thus, invest in

reproduction according to expected winter conditions as they reduced their reproductive allocation

when the environment became more severe. On the other hand, spring body mass declined over

time so population density and winter conditions was limiting factors. Based on this we conclude

that the cost of reproduction for female reindeer has two components. First, a direct cost that

manifested through a lost opportunity for somatic growth during summer. This lost opportunity

for increased autumn body mass will ultimately cause a lowered survival probability, but this will

only happen during especially harsh winters (Tveraa et al. 2003). Thus, the actual cost of

reproduction will be related to expected winter environmental conditions: individuals have no way

of predicting the future so they have to trade somatic growth against reproduction during summer

based an ‘estimated’ distribution of winter conditions based on past experience (Bårdsen et al.

2008). Second, a lagged cost that manifested as a lowering of offspring body mass. As juvenile

survival is more variable and more sensitive to environmental harshness than adult survival

(Gaillard et al. 2000) lowered juvenile body mass will result in reduced reproductive output.

Additionally, individual quality was an important predictor controlled for in all analyses as: (1)

initial body mass can be said to be a true state variable as it was an important predictor in all

analyses, and (2) females producing an offspring in one year showed an increased probability of

producing an offspring in the year to come.


The substantial direct and lagged cost of reproduction as well as the evidence of variation

in individual qualities documented here are in accordance with other studies (e.g. Clutton-Brock et

al. 1989; Dufour and Sauther 2002; Newton 1989) and with the more finding that reproduction is

costly: mammals (Festa-Bianchet et al. 1998; Lambin and Yoccoz 2001; Lummaa and Clutton-

Brock 2002; Sand 1996; Tavecchia et al. 2005; Tveraa et al. 2003), birds (Lindén and Møller 1989;

Monaghan and Nager 1997; Moreno 1989) and plants (Obeso 2002).

Acknowledgments.-- The present study was funded by the Research Council of Norway, the

Norwegian Directorate of Nature Management and the County Authorities of Troms and

Finnmark, Norway. We thank Per M. A. Gaup, Anders I. Gaup, Johannes D. Gaup, Per T. A.

Gaup and Anders A. T. Gaup, as well as their respective families for allowing us to use their

animals in our study and for assisting us in the field. Discussions with John A. Henden, Audun

Stien, Øystein Varpe, Nigel G. Yoccoz, Jan O. Bustnes, Jean M. Gaillard, Anne Loison, Marius W.

Næss, Ingunn M. Tombre and Børge Moe improved the manuscript. David Ingebrigsten, Marius

W. Næss, John A. Henden, Øystein Varpe, Ellen M. Oskal, Ole E. Torland, Audun Stien, Hans

Bjella, Tino Schott, Raymond Sørensen, Siw T. Killengreen, Stein E. Eilertsen and Rune Nilsen

helped us with the fieldwork. We thank Stefano Focardi and two anonymous referee for valuable

comments on the manuscript.

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Table 1. Estimates from linear models (LM) relating female autumn (a) and spring (b) body mass

(kg) as well as offspring (c) body mass (kg) to a set of predictors. The intercept shows mean body

mass for; (1) the level 2002 (a) or 2003 (b-c) for the factor ‘year’, (2) the barren level for the factor

‘reproductive status’ (a-b) or ‘previous reproductive status’ (c) and (3) the level Mieron for the

factor ‘herd’. The other coefficients are the estimated difference between the intercept, or the main

effect for initial body mass, for each level of the other included factors.

Parameter Value (95% CI) t-value P-value

(a) Summer body mass development

Intercept 70.658 (68.797, 72.520) 74.581 <0.001

Spring body mass (BM)a 0.531 (0.447, 0.614) 12.453 <0.001

Reproductive status (RS)b [positive] -4.054 (-6.167, -1.941) -3.769 <0.001

Herd [Njarga] 1.124 (0.346, 1.902) 2.839 0.005

Year [2003] 1.118 (-1.956, 4.192) 0.714 0.475

Year [2004] 1.629 (-1.187, 4.445) 1.137 0.256

Year [2005] 3.012 (0.573, 5.451) 2.427 0.016

Year [2006] 2.977 (0.189, 5.765) 2.098 0.036

Year [2007] 4.405 (1.762, 7.049) 3.274 0.001

RSb [positive] × BMa 0.074 (-0.033, 0.181) 1.358 0.175

RSb [positive] × Year [2003] -1.267 (-4.768, 2.234) -0.711 0.477



RSb [positive] × Year [2006] -5.572 (-8.738, -2.407) -3.459 0.001

RSb [positive] × Year [2007] 0.480 (-2.808, 3.767) 0.287 0.774

R2 = 0.58, F14,480 = 48.10, P < 0.01


Table 1. Continued.


(b) Winter body mass development

Intercept 71.551 (69.732, 73.37) 77.310 <0.001

Previous autumn body mass (BM)c 1.162 (0.997, 1.327) 13.830 <0.001

Previous reproductive status (PRS)d [positive] -0.106 (-2.105, 1.893) -0.100 0.917

Herd [Njarga] -2.347 (-3.724, -0.970) -3.350 0.001

Year [2004] -5.821 (-8.694, -2.948) -3.980 <0.001

Year [2005] -5.617 (-7.977, -3.258) -4.680 <0.001

Year [2006] -6.141 (-8.158, -4.124) -5.980 <0.001

Year [2007] -7.848 (-9.957, -5.740) -7.320 <0.001

Year [2008] -7.284 (-9.531, -5.037) -6.370 <0.001

BMc × PRSd [positive] -0.195 (-0.307, -0.084) -3.440 0.001

BMc × Herd [Njarga] -0.138 (-0.242, -0.034) -2.610 0.009

RS [positive] × Herd [Njarga] 1.902 (0.344, 3.460) 2.400 0.017

BMc × Year [2004] 0.012 (-0.204, 0.228) 0.110 0.913

BMc × Year [2005] 0.079 (-0.094, 0.251) 0.900 0.370

BMc × Year [2006] 0.029 (-0.151, 0.208) 0.310 0.754

BMc × Year [2007] -0.196 (-0.359, -0.033) -2.370 0.018

BMc × Year [2008] 0.013 (-0.185, 0.212) 0.130 0.895

PRSd [positive] × Year [2004] 1.185 (-1.736, 4.105) 0.800 0.426





R2 = 0.82, F21,417 = 87.90, P < 0.01


Table 1. Continued.


(c) Offspring summer body mass development

Intercept 44.082 (41.578, 46.586) 34.980 <0.001

Maternal spring body mass (BM)a 0.476 (0.235, 0.717) 3.930 <0.001

Previous reproductive status (PRS)d [positive] -2.450 (-4.668, -0.233) -2.200 0.031

Year [2004] -3.167 (-5.899, -0.436) -2.300 0.024

Year [2005] -3.567 (-6.278, -0.857) -2.610 0.010

Year [2006] -3.278 (-5.667, -0.889) -2.730 0.008

Year [2007] -0.828 (-3.673, 2.017) -0.580 0.565

BMa × PRS [positive] -0.081 (-0.358, 0.197) -0.580 0.564

R2 = 0.48, F7,90 = 11.90, P < 0.01

aThis variable was measured in April (just before snowmelt).

bRS refers to whether a females was barren (negative) or lactating (positive) during summer.

cThis variable was measured in October or November the year before.

dPRS refers to whether a females was barren (negative) or lactating (positive) the year before.


Table 2. Generalized linear model relating offspring reproduction, i.e. the probability of producing

a calf, as a binary response (i.e. a GLM with binomial family and a logit link function) to a set of

predictors. The intercept shows the logit mean for (1) the level 2002 for the factor ‘year’ and (2)

the barren level for the factor ‘previous reproductive status’. The other coefficients are the

estimated difference between the intercept, or the main effect for initial body mass, for each level

of the other included factors.

Parameter Value (95% CI) z-value P-value

(a) Maternal spring body mass

Intercept 0.941 (0.039, 1.889) 2.000 0.045

Maternal spring body mass (BM)a 0.069 (0.008, 0.139) 2.100 0.036

Previous reproductive status (PRS)b [positive] 0.600 (-0.062, 1.252) 1.800 0.072

Herd [Njarga] -1.071 (-1.715, -0.463) -3.360 0.001

Year [2004] 2.289 (0.904, 4.201) 2.860 0.004

Year [2005] 0.457 (-0.408, 1.318) 1.040 0.297

Year [2006] 1.244 (0.293, 2.234) 2.530 0.011

Year [2007] -0.097 (-1.014, 0.816) -0.210 0.835

BMa × PRSb [positive] 0.003 (-0.081, 0.083) 0.080 0.935

Residual deviance = 345.75, df = 339

Null deviance = 297.36, df = 331


Table 2. Continued.

Parameter Value (95% CI) z-value P-value

(b) Previous maternal autumn body mass

Intercep 1.222 (0.308, 2.195) 2.550 0.011

Previous autumn maternal body mass (BM)c 0.061 (-0.004, 0.132) 1.790 0.074

Previous reproductive status (PRS)b [positive] 0.774 (0.091, 1.454) 2.240 0.025

Herd [Njarga] -1.190 (-1.873, -0.548) -3.540 <0.001

Year [2004] 1.875 (0.483, 3.788) 2.340 0.020

Year [2005] 0.003 (-0.855, 0.844) 0.010 0.995

Year [2006] 0.974 (0.0257, 1.959) 1.990 0.047

Year [2007] -0.472 (-1.356, 0.390) -1.070 0.287

BMc × PRSb [positive] -0.002 (-0.093, 0.087) -0.040 0.965

Residual deviance = 277.58, df = 310

Null deviance = 322.56, df = 318

aThis variable was measured in April (just before snowmelt).

bPRS refers to whether a females was barren (negative) or lactating (positive) the year before.

cThis variable was measured in October or November the year before.


Fig. 1. Time series ( t ; years) of (a) reindeer abundance5 ( ), (b) winter and summer Arctic

Oscillation Index

tN

6 ( ) and (c) precipitation for two coastaltAO 7 (blue) and three continental7

meteorological station (red). The black horizontal line shows where we have detailed individual-

based data (d-f). The reindeer population in this district increased from 2001 peaked at an

historical high abundance in 2005 (arrow). In contrast, climatic conditions have been relatively

stable during the same period. Winter was negative, with the exception of 2007, indicating

that climatic conditions were generally better from 2002-2008 compared to the long-term average6.

Nevertheless, December precipitation in 2006 where approximately double of the monthly normal

values for all stations (arrow; c). Female autumn body mass show no apparent temporal trend (d),

whereas autumn offspring body mass (d), female spring body mass (e) and the proportions of

females giving birth (f; sample size are provided in the figure) decreased as reindeer abundance

increased.

tAO

Fig. 2. Position of summer pastures at the cost and the continental winter pastures in Finnmark,

Norway. Females in the Njarge herd (blue) give birth on their way out to the summer pasture area,

whereas the Mieron herd (red) move to the summer pasture area before the calving season starts.

Rectangles show the position of the meteorological stations (Fig. 1).

Fig. 3. A visualization of the models (re-fitted without centring initial body mass) presented in

Table 1. The left panel show a subset of data from 2006 and the Mieron herd to exemplify data

and the relationship involving initial body mass, RS or PRS and the interaction between them

(Table 1). The right panel shows the temporal trend in estimated body masses for barren and

5 Reindeer abundance data for Silvetnjaraga extracted from official statistics 1981-2007 Anonymous (2007) Ressursregnskap for reindriftsnæringen.

In. Reindriftsforvaltningen, Alta, Norway. 6 Winter AO is the average for monthly values from December (t - 1) to April, whereas summer AO is the June-August average:

http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/teleconnections.shtml. 7 Monthly normal (1961-1990) December precipitation levels (in mm): Tromsø (106), Alta (36), Cuovddatmohkki (18), Dividalen (16) & Sihccajavri

(16): http://www.eklima.no.

http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/teleconnections.shtml

http://www.eklima.no/


lactating females keeping initial body mass constant at population specific averages (68.45 kg for

spring and 66.01 kg for previous autumn body mass).

Fig. 4. A visualization of the models (re-fitted without centring initial body mass) presented in

Table 2. The left panel show a subset of data from 2007 and the Mieron herd to exemplify data

and the relationship involving initial body mass, PRS and the interaction between them (Table 2).

The right panel shows the temporal trend in estimated probabilities for barren and lactating

females keeping initial body mass constant (see Fig. 3 for details). Numbers in the right panel are

showing average body mass for reproducing females in each year.


1980 1985 1990 1995 2000 2005

1200

1400

1600

1800

2000

2200N

t(a) Population dynamics

1980 1985 1990 1995 2000 2005

-3

-2

-1

0

1

2

3

Win

ter A

Ot ±

St.

dev.

(b) Arctic Oscillation (AO)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Sum

mer

AO

t ±

St.

dev.

0

50

100

150

200

Coa

stal

sta

tions

t

(c) December preciptation (mm) TromsøAltaCuovddatmohkkiSihccajavri

Dividalen

10

20

30

40

50

60

Con

tinen

tal s

tatio

nst

1980 1985 1990 1995 2000 2005

2002 2003 2004 2005 2006 2007 2008

66

68

70

72

(d) Autumn body mass (kg)

FemaleOffspring

Body

mas

s t ±

St.

err.

38

40

42

44

2002 2003 2004 2005 2006 2007 2008

62

64

66

68

70

72

(e) Spring female body mass (kg)

Time

0.60

0.65

0.70

0.75

0.80

0.85

0.90

90

66

166

112

96

74

(f) Reproduction (proportional)

Rep

rodu

ctio

n t

2002 2003 2004 2005 2006 2007 2008

(year) t

Fig. 1.


Tromsø

Dividalen

Sihccajavri

Cuovddatmohkki

Alta

FINLANDSWEDEN

NORWAY

Njarga

Mieron

Winter pastures

Summer pastures

SWED

EN

FINL

AND

RUSS

IA

NORW

AY

70° N

60° N

10° E 30° E

Fig. 2.


40 50 60 70 80

45

50

55

60

65

70

75

80

Spring body mass (kg)

Autu

mn

body

mas

s (k

g)(a)

BarrenLactating

2002 2003 2004 2005 2006 2007

64

66

68

70

72

74

76 (b)

60 65 70 75

55

60

65

70

75

80

Previous autumn body mass (kg)

Sprin

g bo

dy m

ass

(kg)

(c)

2003 2004 2005 2006 2007 2008

Aver

age

body

mas

s ±

St.

err.

64

66

68

70

72(d)

60 65 70 75

35

40

45

50

Maternal spring body mass (kg)

Offs

prin

g au

tum

n bo

dy m

ass(

kg)

(e)

Barren previous yearLactating previous year

2003 2004 2005 2006 2007

Time (year)

38

40

42

44

(f)

Fig. 3.


50 60 70 80

0.0

0.2

0.4

0.6

0.8

1.0

Maternal spring body mass (kg)

(a)

Barren previous yearLactating previous year

2003 2004 2005 2006 2007

0.6

0.7

0.8

0.9

1.0

72.6

68.1

65.9

67

64.8

50 55 60 65 70 75 80

0.0

0.2

0.4

0.6

0.8

1.0

Previous autumn body mass (kg)

(c)

2003 2004 2005 2006 2007

Time (year)

0.6

0.7

0.8

0.9

1.0 (d)

68.8

71.1

67

69.2

64.8

Aver

age

prob

abilit

y ±

St.

err.

Prob

abilit

y (r

epro

duct

ive

succ

ess)

Fig. 4.

Risk sensitive reproductive allocation

S1.1

S1: STATISTICAL ANALYSIS – PREDICTIONS, CONFOUNDING AND POSSIBLE

SPURIOUS EFFECTS

As this is an observational study there are several confounding factors that can potentially induce

bias in our analyses, but this problem is reduced to a minimum. First, we reduced the probability

of pursuing spurious effects (Anderson et al., 2001) as we had a priori expectations that formed the

basis for the set of candidate models in which we selected the most parsimonious model (e.g.

Anderson, Burnham & Thompson, 2000; Buckland, Burnham & Augustin, 1997; Burnham &

Anderson, 2002). Second, we applied statistical control of initial body mass in order to assess

temporal correlation in body mass, i.e. to ‘reset our system to a given time’ (Fig. S1.1). The

biological rationale for this was that we assess mass development from one point in time to another.

Moreover, by providing statistical control for initial body mass we also control for potential

confounders like: (1) lagged and current reproductive success and reproductive allocation (Bårdsen

et al., 2008; Cameron et al., 1993; Fauchald et al., 2004; Kojola, 1993); (2) age (Kojola et al., 1998;

Reimers, Klein & Sorumgard, 1983; Rødven, 2003); (3) survival (Tveraa et al., 2003); (4) parasitic

infestation (Fauchald et al., 2007); (5) social rank (Holand et al., 2004; Kojola, 1989); and (6)

population density and environmental conditions (Fauchald et al., 2004; Kumpula, Colpaert &

Nieminen, 1998; Tveraa et al., 2007). We lack information on many of the above factors, but have

information on age. Three age-classes, i.e. the juvenile, adult and senescent stage, has generally

been identified for large-herbivores (Gaillard et al., 2000: Fig. 1). As reindeer are harvested we do

not have senescent individuals in our study. Juveniles (≤1 year) was smaller in the spring compared

to the older classes (B.-J. Bårdsen, T. Tveraa, P. Fauchald & K. Langeland, unpublished results),

and as they are not sexually mature we removed them from the data. Consequently, the analyses in

the present study focus on the prime-aged segment of the adult stage. Third, even though we do

not provide information about density or environmental conditions directly in the analyses these

effects are at least partly controlled for by our inclusion of year and herd (Fig. 1-2). In essence, as


S1.2

we based our analyses on a priori expectations and because we provided statistical control for initial

body mass, year and herd we are confident that our analyses are robust.

LITERATURE CITED

Anderson, D.R., Burnham, K.P., Gould, W.R., & Cherry, S. (2001) Concerns about finding effects that are actually spurious. Wildlife Society Bulletin, 29, 311-316.

Anderson, D.R., Burnham, K.P., & Thompson, W.L. (2000) Null hypothesis testing: problems, prevalence, and an alternative. Journal of Wildlife Management, 64, 912-923.

Buckland, S.T., Burnham, K.P., & Augustin, N.H. (1997) Model selection: an integral part of inference. Biometrics, 53, 603-618.

Burnham, K.P. & Anderson, D.R. (2002) Model selection and multimodel inference: a practical information-theoretic approach, Second edn. Springer, Inc., New York, USA.

Bårdsen, B.-J., Fauchald, P., Tveraa, T., Langeland, K., Yoccoz, N.G., & Ims, R.A. (2008) Experimental evidence for a risk sensitive life history allocation in a long-lived mammal. Ecology, 89, 829-837.

Cameron, R.D., Smith, W.T., Fancy, S.G., Gerhart, K.L., & White, R.G. (1993) Calving success of female caribou in relation to body weight. Canadian Journal of Zoology, 71, 480-486.

Fauchald, P., Rødven, R., Bårdsen, B.-J., Langeland, K., Tveraa, T., Yoccoz, N.G., & Ims, R.A. (2007) Escaping parasitism in the selfish herd: age, size and density-dependent warble fly infestation in reindeer. Oikos, 116, 491-499.

Fauchald, P., Tveraa, T., Henaug, C., & Yoccoz, N. (2004) Adaptive regulation of body reserves in reindeer, Rangifer tarandus: a feeding experiment. Oikos, 107, 583-591.

Gaillard, J.M., Festa-Bianchet, M., Yoccoz, N.G., Loison, A., & Toïgo, C. (2000) Temporal variation in fitness components and population dynamics of large herbivores. Annual Review of Ecology and Systematics, 31, 367-393.

Holand, O., Gjøstein, H., Losvar, A., Kumpula, J., Smith, M.E., Røed, K.H., Nieminen, M., & Weladji, R.B. (2004) Social rank in female reindeer (Rangifer tarandus): effects of body mass, antler size and age. Journal of Zoology, 263, 365-372.

Kojola, I. (1989) Mothers dominance status and differential investment in reindeer calves. Animal Behaviour, 38, 177-185.

Kojola, I. (1993) Early maternal investment and growth in reindeer. Canadian Journal of Zoolog, 71, 753-758.

Kojola, I., Helle, T., Huhta, E., & Niva, A. (1998) Foraging conditions, tooth wear and herbivore body reserves: a study of female reindeer. Oecologia, 117, 26-30.

Kumpula, J., Colpaert, A., & Nieminen, M. (1998) Reproduction and productivity of semidomesticated reindeer in northern Finland. Canadian Journal of Zoology, 76, 269-277.


S1.3

Reimers, E., Klein, D.R., & Sorumgard, R. (1983) Calving time, growth rate, and body size of Norwegian reindeer on different ranges. Arctic and Alpine Research, 15, 107-118.

Rødven, R. (2003) Tetthet, klima, alder og livshistorie i en tammreinflokk i Finnmark, University of Tromsø, Tromsø, Norway. [in Norwegian]

Tveraa, T., Fauchald, P., Henaug, C., & Yoccoz, N.G. (2003) An examination of a compensatory relationship between food limitation and predation in semi-domestic reindeer. Oecologia, 137, 370-376.

Tveraa, T., Fauchald, P., Yoccoz, N.G., Ims, R.A., Aanes, R., & Høgda, K.A. (2007) What regulate and limit reindeer populations in Norway? Oikos, 116, 706-715.


S1.4

(a) 'Silly' null-model

Equation:yi = αBa rren +x iβBa rre n

yi = αL a cta t i n g + xiβL act at i n g

Parameters:αBa rre n = αL a cta t i ng = y i

βBa rre n = βL a cta t i ng = 0

(b) RS (main effect) + body masst−1

Parameters:αBa rren > αL act a t i n g

βBa rren = βL a ct a t i n g

Barren

Reproductive status (RS)

Lactating

Reproductive status (RS)

(c) Body masst−1 ×RS

Parameters:αBa rre n = αL a cta t i n g

βBa rre n > βL a cta t i n g

(d) RS + body masst−1 ×RS

Parameters:αBa rren < αL act a t i n g

βBa rren > βL a ct a t i n g

Body masst−1 (xi )

Bod

y m

ass t

(yi)

Fig. S1.1. A graphical representation of possible predictions in the analyses of body mass. Body mass in any point in

time ( ) can be a function of body mass earlier (t 1−t ; hereafter termed initial body mass) and reproductive status

(hereafter RS; ‘barren’ versus ‘lactating’). The two equations (a) show how separate models, defined by the parameters

α and β , can be used to predict the relationship between and across the RS groups. (a) The null-model, where

body mass is not explained by neither RS nor initial body mass; both the intercept (

iy ix

α ), equaling the average of the

predictor, and the slope (β ), equaling zero, is similar across the RS groups. (b) The main-effect model, where mean body

mass is different across the RS groups: α is now higher for barren compared to lactating females, but β is similar.

The dotted grey line shows the predicted relationship for α = 0 and β = 1, which indicates where = . Above

this line individuals have gained body mass and below this line they have lost body mass between t and . (c) The

initial body mass × RS model, where the relationship between initial body mass and body mass is different across the RS

groups:

i

1

y

−

ix

t

α is equal across the groups, but β is higher for barren compared to lactating females. (d) The main-effect and

interaction model, where both mean body mass and the relationship between initial body mass and body mass is different

across the RS groups: α is higher for lactating compared to barren females whereas forβ the difference is opposite.

Risk sensitive reproductive allocation S2.1

S2: MODEL SELECTION & THE SET OF CANDIDATE MODELS IN THE

ANALYSES OF BODY MASS

Selecting the models used for inference in the three analyses presented in Table 1 was performed

within a model selection framework (e.g. Anderson et al. 2000; Buckland et al. 1997; Burnham and

Anderson 2002): First, a pool of candidate models was defined. Defining the set of candidate

models is an important but often underemphasized part of an statistical analysis: ‘models without

biological support should not be included in the set of candidate models’ (Burnham and Anderson

2002). Thus, we kept initial body mass (either spring or autumn females body mass), reproductive

status or previous reproductive status [factor with two levels: ‘negative’ (barren) or ‘positive’

(lactating) during either summer or last year], and the interaction between the two in all analyses

based on our a priori expectations (see Table S1.1-3 for details). Second, in each analysis, rescaling

and ranking models relative to the value of the model with the lowest second-order Akaike’s

Information Criterion (AICc1) value was performed (Burnham and Anderson 2002: Δi denotes this

difference for model i ).

LITTERATURE CITED

Anderson DR, Burnham KP, Thompson WL (2000) Null hypothesis testing: problems, prevalence, and an alternative. Journal of Wildlife Management 64:912-923

Buckland ST, Burnham KP, Augustin NH (1997) Model selection: an integral part of inference. Biometrics 53:603-618

Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, Second edn. Springer, Inc., New York, USA.

1 AICc is often called a small sample size adjusted Akaike’s Information Criterion (AIC). If the sample size (n) is large

relative to the number of parameters (K), a model’s AICc value will converge towards its AIC value (Burnham and Anderson2002).


Table S1.1. The relative evidence for each candidate model (i) in Table 1a based on differences in

AICc values (Δi). The model in underlined italics were selected and used for inference in each

analysis as it was the simplest models with an Δi ≤ 1.5). The predictors included in the different

models are marked with an ‘x’.

i

Spri

ng

bod

y m

ass

(BM

)a

Rep

rod

uct

ive

stat

us

(RS)

a

BM

× R

Sa

Her

d (H

)a

Yea

r (Y

)a

BM ×

H

RS ×

H

BM ×

Y

RS ×

Y

H ×

Y

BM ×

RS

× H

BM ×

RS

× Y

BM ×

H ×

Y

RS ×

H ×

Y

BM ×

RS

× H

× Y

Kb Δi

1. x x x x x x x x x x x x x x x 48 36.52 2. x x x x x x x x x x x x x x 44 25.89 3. x x x x x x x x x x x x x 43 23.75 4. x x x x x x x x x x x x 38 21.07 5. x x x x x x x x x x x 33 17.92 6. x x x x x x x x x x 28 18.05 7. x x x x x x x x x 23 14.10 8. x x x x x x x x 22 12.03 9. x x x x x x x 17 2.02 10. x x x x x x 16 0.00

11. x x x x x 11 7.17 12. x x x x 10 11.77 13. x x x 5 71.93

aThe predictors to the left in bold were kept in all models based on our a priori expectations.

bK denotes the number of parameters, whereas the number of observations (n) was 495 for all

models.


Table S1.2. The relative evidence for each candidate model (i) in Table 1b based on differences in




i

Au

tum

n b

ody

mas

s (B

M)a

Pre

viou

s au

tum

n

rep

rod

uct

ive

stat

us

(RS)

a

BM

× R

Sa

Her

d (H

)a

Yea

r (Y

)a

BM ×

H

RS ×

H

BM ×

Y

RS ×

Y

H ×

Y

BM ×

RS

× H

BM ×

RS

× Y

BM ×

H ×

Y

RS ×

H ×

Y

BM ×

RS

× H

× Y

Kb Δi

1. x x x x x x x x x x x x x x x 40 12.74 2. x x x x x x x x x x x x x x 37 7.89 3. x x x x x x x x x x x x x 36 10.18 4. x x x x x x x x x x x x 32 13.24 5. x x x x x x x x x x x 28 5.05 6. x x x x x x x x x x 24 0.00 7. x x x x x x x x x 20 0.78

8. x x x x x x x x 19 5.65 9. x x x x x x x 15 10.74 10. x x x x x x 14 17.18 11. x x x x x 10 14.63 12. x x x x 9 18.60 13. x x x 5 167.075



models.


Table S1.3. The relative evidence for each candidate model (i) in Table 1c based on differences in




i

Mat

ern

al s

pri

ng

bod

y m

ass

(BM

)a

Pre

viou

s au

tum

n

rep

rod

uct

ive

stat

us

(RS)

a

BM

× R

Sa

Her

d (H

)a

Yea

r (Y

)a

BM ×

H

RS ×

H

BM ×

Y

RS ×

Y

H ×

Y

BM ×

RS

× H

BM ×

RS

× Y

BM ×

H ×

Y

RS ×

H ×

Y

BM ×

RS

× H

× Y

Kb Δi

1. x x x x x x x x x x x x x x x 30 90.30 2. x x x x x x x x x x x x x x 29 68.01 3. x x x x x x x x x x x x x 28 62.87 4. x x x x x x x x x x x x 27 43.80 5. x x x x x x x x x x x 24 29.52 6. x x x x x x x x x x 21 19.36 7. x x x x x x x x x 18 9.75 8. x x x x x x x x 17 12.90 9. x x x x x x x 14 4.77 10. x x x x x x 13 2.97 11. x x x x x 10 1.48 12. x x x x 9 0.00

13. x x x 5 3.48



models.


S3: MODEL SELECTION & THE SET OF CANDIDATE MODELS IN THE

ANALYSES OF OFFSPRING PRODUCTION

Table S3.1. The relative evidence for each candidate model (i) in Table 2a based on differences in

AICc values (Δi; see S2 for details). The model in underlined italics were selected and used for

inference in each analysis as it was the simplest models with an Δi ≤ 1.5). The predictors included

in the different models are marked with an ‘x’.

i

Mat

ern

al s

pri

ng

bod

y m

ass

(BM

)a

Pre

viou

s au

tum

n

rep

rod

uct

ive

stat

us

(RS)

a

BM

× R

Sa

Her

d (H

)a

Yea

r (Y

)a

BM ×

H

RS ×

H

BM ×

Y

RS ×

Y

H ×

Y

BM ×

RS

× H

BM ×

RS

× Y

BM ×

H ×

Y

RS ×

H ×

Y

BM ×

RS

× H

× Y

Kb Δi

1. x x x x x x x x x x x x x x x 40 31.59 2. x x x x x x x x x x x x x x 36 24.77 3. x x x x x x x x x x x x x 35 32.31 4. x x x x x x x x x x x x 31 27.42 5. x x x x x x x x x x x 27 23.73 6. x x x x x x x x x x 23 17.57 7. x x x x x x x x x 19 12.62 8. x x x x x x x x 18 10.91 9. x x x x x x x 14 6.55 10. x x x x x x 13 4.44 11. x x x x x 9 0.00

12. x x x x 8 10.13 13. x x x 4 22.34



models.


Table S3.2. The relative evidence for each candidate model (i) in Table 2b based on differences in

AICc values (Δi; see S2 for details). The model in underlined italics were selected and used for

inference in each analysis as it was the simplest models with an Δi ≤ 1.5). The predictors included

in the different models are marked with an ‘x’.

i

Mat

ern

al p

revi

ous

autu

mn

b

ody

mas

s (B

M)a

P

revi

ous

autu

mn

re

pro

du

ctiv

e st

atu

s (R

S)a

BM

× R

Sa

Her

d (H

)a

Yea

r (Y

)a

BM ×

H

RS ×

H

BM ×

Y

RS ×

Y

H ×

Y

BM ×

RS

× H

BM ×

RS

× Y

BM ×

H ×

Y

RS ×

H ×

Y

BM ×

RS

× H

× Y

Kb Δi

1. x x x x x x x x x x x x x x x 39 41.46 2. x x x x x x x x x x x x x x 36 34.30 3. x x x x x x x x x x x x x 35 36.43 4. x x x x x x x x x x x x 31 29.01 5. x x x x x x x x x x x 27 28.17 6. x x x x x x x x x x 23 19.32 7. x x x x x x x x x 19 13.55 8. x x x x x x x x 18 11.71 9. x x x x x x x 14 7.22 10. x x x x x x 13 5.18 11. x x x x x 9 0.00

12. x x x x 8 11.56 13. x x x 4 21.64



models.

PAPER 4

Plastic reproductive allocation as a buffer

against environmental unpredictability –

linking life history and population

dynamics to climate

Bårdsen, B.-J., J.-A. Henden, P. Fauchald, T. Tveraa & A. Stien

Manuscript

Running head: Plastic reproductive allocation and environmental unpredictability

Title: Plastic reproductive allocation as a buffer against environmental unpredictability – linking life

history and population dynamics to climate

List of authors: Bård-Jørgen Bårdsen a ,b ,1, John Andrè Henden b,2, Per Fauchald a,b,3, Torkild Tveraa

a,4 & Audun Stien a,5

a Norwegian Institute for Nature Research (NINA), Division of Arctic Ecology, Polar Environmental Centre, N-9296

Tromsø, Norway.

b University of Tromsø (UIT), Department of Biology, N-9037 Tromsø, Norway.

1 [email protected] (author for correspondence)

2 [email protected]

3 [email protected]

4 [email protected]

5 [email protected]







Plastic reproductive allocation and environmental unpredictability 2

Abstract: Organisms adopt a risk sensitive reproductive allocation when summer reproductive

allocation competes with survival in the coming winter. Autumn female body mass, which

represents an insurance against unpredictable winter conditions, is traded against reproductive

allocation during summer. In our model, climate had large effects on individual optimization as:

(1) Dynamic strategies were needed to buffer climate effects. (2) Females were risk averse, as

strategies involving a low reproductive allocation per unit female spring body, had the highest

fitness under unpredictable and poor environmental conditions. These strategies resulted in high

expected female age and adult body size in harsh environments. (3) Negative density dependence

had a strong negative effect on offspring body mass and survival. This effect was larger than

negative effects of climate so we did not find clear negative effects of environmental conditions

on reproduction. (4) Moreover, the optimal reproductive strategies together with environmental

conditions had significant impact on population dynamics. First, populations inhabiting benign

environments were most sensitive to climatic perturbations due to their characteristically high

density, which limited the possibility for individuals to buffer adverse climatic effects. Second,

populations inhabiting harsh environments were least sensitive to climatic perturbations. Winter

conditions ‘harvested’ these populations, especially younger individuals, with the consequence of

releasing these populations from negative density dependence resulting in a high reward for a

given allocation.

Key words: evolution; environmental stochasticity; individual based modeling (IBM); phenotypic

plasticity; prudent parent; Rangifer tarandus; risk sensitive life histories; time-series.


INTRODUCTION

A central issue in life-history theory is how individuals allocate resources between current

reproduction and future survival, a trade-off known as the cost of reproduction (e.g. Roff 1992,

Stearns 1992). Recent studies suggest that severe climatic conditions may have a strong impact on

the cost of reproduction in large mammals (Clutton-Brock and Pemberton 2004). The effect of

environmental stochasticity on the cost of reproduction and life-history evolution is generally

poorly understood except that long-lived organisms are known for favoring own survival over

reproduction (Gaillard et al. 1998, Gaillard et al. 2000, Gaillard and Yoccoz 2003).

Many organisms inhabit highly unpredictable environments caused by temporal variation in

abiotic weather conditions and/or biotic factors such as population density (e.g. McNamara et al.

1995, Clutton-Brock et al. 1996, Coulson et al. 2001, Tveraa et al. 2007). Environmental

variability usually consists of both predictable seasonal trends and unpredictable stochastic

variation around this trend. Consequently, organisms have to make behavioural decisions in one

season without full knowledge about future environmental conditions (e.g. McNamara et al.

1995, Bårdsen et al. 2008). If, for example, the winter season represents a bottleneck for survival

and winter weather conditions are highly variable, individuals ensure that they retain sufficient

reserves during summer in order to survive the coming winter (see Erikstad et al. 1998, Bårdsen

et al. 2008). If reproduction also takes place during summer they have to balance reproductive

allocation during summer, when, in fact, they pay a delayed cost of reproduction in the coming

winter. Formally, this means that behavioural decisions has to be taken before the future state of

the environment is known.

When reproduction competes with the amount of resources available for survival during an

unpredictable non-breeding season, individuals should adopt a risk sensitive regulation of their

reproductive allocation (see Stephens and Krebs 1986, Kacelnik and Bateson 1996 and references


therein for a discussion of the concept of risk sensitivity, Bårdsen et al. 2008, provide details on

risk sensitive reproductive allocation) For a given distribution of winter conditions, a risk prone

reproductive strategy involves high reproductive allocation that will result in high reproductive

rewards during benign winters but a high survival cost during harsh winters. A low reproductive

allocation will, on the other hand, result in consistently high winter survival and represents a risk

averse reproductive strategy. Organisms that experience stable and benign winter conditions can, thus,

afford high reproductive allocation during summer and low autumn body reserves, whereas

organisms experiencing harsh and variable winter conditions lower their reproductive allocation

to retain higher autumn body reserves. Adopting a risk averse life history is typical for e.g.

temperate large-herbivores where reproductive allocation competes with acquisition and

maintenance of body reserves during summer. For these organisms autumn body mass functions

as an insurance against stochastic winter climatic severity (Reimers 1972, Skogland 1985, Clutton-

Brock et al. 1996, Fauchald et al. 2004, Bårdsen et al. 2008).

The quantity and quality of studies using climate modeling, especially models with a high spatial

resolution, have increased over recent years (Tebaldi et al. 2006). By providing future climate

scenarios, this branch of science plays an important role in the current debate on potential

consequences of future climate change. Scenarios for future climate change generally predict an

increase in the average, the variance and even a changed distribution of important climatic

variables like precipitation and temperature (e.g. Rowell 2005, Sun et al. 2007). Nevertheless,

these changes are predicted to vary both temporally (e.g. Rowell 2005, Tebaldi et al. 2006) and

spatially (e.g. Hanssen-Bauer et al. 2005, Rowell 2005, Tebaldi et al. 2006, Sun et al. 2007). How

living organisms will respond to these predicted climate changes is unclear as current empirical

results are based on climatic effects given the current distribution of important climate variables,

but some predictions has been made. For example, on a population-level, predicted

consequences of future climate change commonly invoke more frequent population collapses


(e.g. Post 2005). Such predictions are problematic as they generally assume a non-plastic life

history in the sense that organisms cannot adapt to new climatic regimes (e.g. Bårdsen et al.

2008). We suggest that on the risk prone-risk averse continuum, more risk averse strategies

should have a stabilizing effect on population dynamics leading to reduced temporal variation in

population density as individuals adjust their reproductive allocation to buffer adverse climatic

effects (Tveraa et al. 2007, Bårdsen et al. 2008). Within the concept of risk sensitivity it is the

variance, i.e. the predictability, in climatic variables that important. In fact, most studies on this

subject have been performed on two or several experimental groups being subject to the same

average reward where manipulation have consisted of rewards associated with different levels of

variability (‘the standard design of risk sensitive experiments’: reviewed by e.g. Stephens and

Krebs 1986, Kacelnik and Bateson 1996).

The objective of this study is to investigate the effects of different types of environment on

reproductive strategies in long-lived mammals and to investigate how the interaction between the

optimal strategy and the environment shape population dynamics. We have previously tested

some of these concepts empirically on reindeer (or caribou; Rangifer tarandus; see below). Reindeer

represents a suitable model organism for these questions as: (i) female reindeer give birth to only

one offspring per year; (ii) reindeer occupy a wide range of different environments covering

several continents; and (iii) reindeer are a long-lived organisms where both survival and

reproduction are positively related to body size (Kojola 1993, 1997, Tveraa et al. 2003, Fauchald

et al. 2004, Bårdsen et al. 2008). Moreover, female reindeer gain body mass during summer in

order to buffer harsh winter conditions (Bårdsen et al. 2008): reindeer who start harsh winters on

low body reserves can experience a drastic reduction in subsequent survival (Tveraa et al. 2003).

The present study, which is a follow-up to previous empirical studies (Tveraa et al. 2003,

Fauchald et al. 2004, Tveraa et al. 2007, Bårdsen et al. 2008), use a state-dependent individual-

based model (IBM) to investigate how females should optimize their reproductive allocation in a


stochastic environment that contains density dependent processes. This study will give us

answers to the following research questions: (1) How does the average and variance in

environmental conditions affect the optimal reproductive allocation and (2) how do different

reproductive allocation strategies affect vital rates and population dynamics for a given

environment?

THE INDIVIDUAL-BASED MODEL (IBM)

Model overview

The IBM developed in the present study is a stochastic density-dependent model where we test if

different types of stochastic winter environments have an effect on the optimal reproductive

strategy and to what extent it is an interaction between the chosen optimal strategy and

environmental conditions in shaping population dynamics. The model excludes males (with an

assumed sex ratio of 0.5 at birth) because the focus here is on female life-history traits and

because important parameters are widely available for females but not for males. We are, thus,

dealing with the female segment of a population over several years; time ( t ) is discrete (one step

equals one year), each step is divided in two distinct seasons: (i) summer where density dependent

competition among individuals over a shared food resource occur; and (ii) winter where

stochastic environmental conditions affects survival and mass losses. The model will be run for

time steps (from to ). Individual state variables include age ( ; year) and body

mass (kg). Population-level state variables include summer density ( ; individuals km-2) and

winter environmental conditions ( ; relative scale where ‘less is better’ in the sense that the large

positive values represents harsh conditions, which is similar to climatic indexes like AO and

NAO). A key point in this model is that individuals do not know the state of the coming winter

conditions ( ) at the time when reproductive allocation takes place. Consequently, even though

processes that affect individuals in one season will have effects in the coming season it is crucial

T 0tt = Ttt += 0

E

j

D

E


that these processes are treated independently in the model. A detailed description, which follows

the ‘overview, design concepts and details’ (ODD) protocol developed by Grimm et al. (2006)

and Grimm & Railsback (2005) is found in A1. Formalities, like model equations, rules and tables

presenting the model parameters, are presented in the ODD protocol (A1). All simulations,

statistical tests and plotting were performed in the software R (R Development Core Team 2007).

Since seasonality is the key to understand reproductive allocation strategies in reindeer (Bårdsen

et al. 2008) we will give a short overview of the model separated by season (see Figure 1 for

schematic overview of processes and scheduling).

Summer (1 May to 31 October: 184 days)

An allocation strategy will at any point in time be a scalar representing an individual’s allocation

of resources, i.e. spring body mass, to reproduction vs. somatic growth, which is a proxy for

survival, during summer. An individual can only invest in reproduction ( ) and survival ( ); i.e.

. The reward for a fixed allocation will be limited by the population’s summer density

( ). That is, an individual with a fixed reproductive allocation strategy will collect a higher

average reproductive reward in low- vs. high-density environments. Consequently, the reward of

investing in and will be implemented in two functions (see A1: Autumn body mass and

Gain function sections): (1) one gain function for females where and are predictors and (2)

one function for offspring where and are predictors. In sum, individual autumn body mass,

i.e. summer mass development, depends on (Figure 1): (1) spring body mass (in the first year of

life this will be an individual’s birth mass), (2) the gain function that represents the increase in

body mass per kg spring mass, and (3) a basal summer metabolic rate (

R

D

S

S

1=+ SR

D

R S

S

R D

β ). Generally, for

individual i of age at time this relationship can be represented by the following equation

(modified from Proaktor et al. 2007):

j t

( )tjitjitjiti Sbmtjibmbm SpringGainSpringAutumn

,,,,,,,1, ,, β−×+= . eqn. 1


Winter (1 November to 31 April: 181 days)

Autumn body mass ( ) is a predictor of the three processes that happens in the autumn

and during winter: (1) If is below a threshold (

bmAutumn

Autumnbm autumnτ ) the individual is assumed dead

during summer and is removed from further analyses. (2) If > bmAutumn autumnτ , and

winter conditions (

bmAutumn

E ) is a predictor of individual winter survival probability [ ].

(3) If an individual survives the winter, its body mass next spring ( ) will depend on

as well as a winter loss of body mass (

( )femaleSurvival |P

1+tbmSpring

tbmAutumn Wβ ). After these processes have been run, time

will go one step forward (from t to 1+t ) and the following parameters will be updated (Figure

1); (1) mortality [ ], (2) spring body mass ( ), (3) age ( ) and (4)

population density ( ).

(Survival |

D

)femaleP bmSpring j

Reproductive investment strategies

The heart of this IBM is how reproductive allocation strategies, which define the relationship

between survival vs. reproduction, are defined (Figure 2). When modeling life history strategies

one must define what actions are available to an organism, and how the consequence of an action

depends on the action itself, the organism’s state and the environment (McNamara 1997). In this

model, individuals have a built-in reproductive strategy, which defines a behavioural algorithm or

rule, which an individual has to follow. An individual ( i ) of age ( ) will at a given time (j t )

allocation a proportion of its available resources in reproduction ( ). Juveniles ( ) do not

invest in reproduction. This ensures that juveniles invest everything in somatic growth. Note that

reproductive allocation is defined on a continuous scale as is a scalar defined within the

closed interval: . Investment in somatic growth, a proxy for survival, is then:

tji ,,R 1≤j

tjiR ,,

[ ]1,0,, =tjiR

0,1, =≤ tjiR if 1≤j . eqn. 2

tjitji RS ,,,, 1−= . eqn. 3


As total energy allocation sums to one, individuals either invest in reproduction or

survival and nothing else. The model contain no true senescence (as e.g. the IBM by Proaktor et

al. 2007), but age is an important individual-level state variable as it ensures that juveniles do not

reproduce and that females do not become unrealistic old. The cost and benefit, assuming a

constant female body mass, for different as a function of density and winter weather

condition is shown in Figure 2. Two types of strategies were tested against each other in the

simulations.

jiR ,

Fixed reproductive strategies (FS)

A fixed strategy (FS) is defined as a scalar between 0 and 1 that represents an allocation rule that an

individual will follow throughout its adult life. This type of strategy can simply be defined by a

vector such as e.g. [ ]... 0.4, 0.4, 0.4, 0.0,=iR , which means that this individual will invest zero in

reproduction its first year of life, and then 0.4 for the rest of its life.

Dynamic state dependent reproductive strategies (DSDS)

As body mass is a very important predictor for both survival and reproductive output for female

Rangifer (Kojola 1993, 1997, Tveraa et al. 2003, Fauchald et al. 2004, Bårdsen et al. 2008) it is

natural that spring body mass acts as a state variable in the model. Thus, in a dynamic state dependent

reproductive strategy (DSDS) will be determined and updated each year according to the

following equations (see A1):

tjiR ,,

( )[ ]tjibmRR Springbatjie

R,1,1

1,,

>×+−

+= if 1>j & if springbm tji

Spring τ>< ,1, eqn. 4

0,, =tjiR . if 1≤j or if springbm tjiSpring τ≤

< ,1, eqn. 5

In order to invest in reproduction, females must be older than the juvenile stage ( ) and they

must have a spring body mass ( ) above a lower threshold value (

1>j

tjibmSpring,, springτ ). The intercept

( ) in the equation is constant (Table A1.1) among strategies so that a DSDS can in a simplified Ra


way be defined as by the parameter (A1). The inclusion of a lower body mass thresholds

above, which females invest in reproduction, and below, which they do not, has been found in

several long-lived mammals such as red deer Cervus elaphus (Albon et al. 1983), moose Alces alces

(Sæther and Haagenrud 1983, Sæther et al. 1996), bighorn Ovis canadensis (Jorgenson et al. 1993)

and reindeer (Reimers 1983, Skogland 1985, Tveraa et al. 2003). Depending on how an

individual’s spring body mass develops over time, reproductive allocation following a DSDS may

end up looking like e.g. over 5 time steps. Both the FS and the DSDS

strategies are in one sense pure as reproductive allocation is totally given by age (FS & DSDS)

and spring body mass (DSDS), but they may also be considered mixed as both adult and

offspring survival is probabilistic (Houston and McNamara 1999).

Rb

[ 0.7,

( yx ,

] 0.0,0.4 0.4, 0.0,=iR

)NE ≈

Design

We will answer our research questions by running the model under normally distributed

environmental conditions [ ] characterized by different theoretical averages ( ; low

values represent environments that can be characterized as good whereas high values represent

poor ones) and theoretical standard deviations (

x

y ; synonymous to unpredictability) (Figure A1.2).

We applied three different theoretical averages ( 15.0,15.0,00.0 −=x ) termed ‘control’, ‘improved’

& ‘reduced’, and 41 different theoretical standard deviations ( 00.2,...,10.0,05.0,00.0=y ). This

gives a total of 123 possible simulations ( yx × ). Populations went extinct before convergence

when y > 1.55 so we ended up with a total of 90 simulations. E was generated using the rnorm

function in R (R Development Core Team 2007).

A simulation is said to converge when one winning strategy is left alone. After this happened, we

ran the simulation for 20 more years as to ‘harmonize’ the dynamic between the individuals,

which follows the same strategy, in the population and environmental conditions: after this the

simulation was run for another 60 years when terminal time (T ) was reached and the simulation


was terminated. We collected ‘pseudo-empirical’ data on important output during the last 60

years of each simulation (see A2 for an example simulation). T for each simulation was

dependent on both and x y (A3). This, however, was not the case for the estimated values of x

(hereafter termed environmental average or simply E ) and (ii) y [hereafter termed

environmental stochasticity or simply ( )E dev. st. ] who simply were related to their respective

theoretic input values ( & ; A3). x y

Pseudo-empirical statistical analyses

Investment in reproduction and survival

Each simulation output consisted of 60-years of data on environmental conditions, female

reproductive success (number of offspring per female) and population spring density, spring and

autumn body mass of both offspring and females as well as female reproductive and somatic

allocation ( R & S ). We analysed these generated datasets by standard statistical approaches.

First, within simulations we fitted a linear model where each yearly average ( ) was predicted

based on the centred value (subtracting the average) for environmental conditions for the last

winter ( )

tvalue

tE 6. Second, we fitted generalized additive models (GAM), using the mgcv library

(Wood 2008), using the intercepts ( ) from the ‘within simulations analyses’ above as

responses in an ‘across simulation analyses’. We then used the smoothened interaction between

both environmental characteristics [i.e.

intersept

( )E dev. st. & E ] and smoothened D was used as

predictors (Wood 2006)7. Both smooth terms in the GAM were estimated using thin plate

regression splines, which means that the degree of complexity within the limits set by ‘k’ was

selected objectively (Wood 2006: 152-160, 226).

6 Within simulation analyses.-- In R each yearly value (t) was modelled as follows: ‘lm( ~ I valuet ⎟⎠⎞⎜

⎝⎛ − EtE )’. Centring of environmental conditions

means that the intercept in such an analysis represents the estimated, or predicted, values for the average environment for that simulation. 7 Across simulation analyses.-- In R the intercept from each analysis above was predicted as follows: ‘gam( ~ s( ,intersept ( )E dev. st. E , bs="tp",

k=k*3) + s( R , bs="tp", k=k) )’ where ’k ’ equals 4.


Population dynamics and time series analyses

In all time series analyses we adopted the same analytical approach as Tveraa et al. (2007).

Consequently, we estimated the density dependent and density independent structure in each

population time series by fitting second-order autoregressive models [AR(2)] (as described in e.g.

Shumway and Stoffer 2006, Cryer and Chan 2008). We focus on modelling population growth

rate, i.e. ( ttet XX 1log += )λ , to avoid problems associated with temporal trends, i.e. non-stationary,

in the time series (Cryer and Chan 2008). The linear predictor of the models included the effects

of direct density-dependence, delayed density dependence with a lag of one time step ( ) and

the direct effect of on

1−t

tE tλ [formally we have used an ARIMA(p = 2, d = 0, q = 0) model; the

arima function in R (e.g. Ripley 2002, Shumway and Stoffer 2006, Cryer and Chan 2008); E as

a covariate was included via the xreg argument]. We, thus, estimated the first-order AR

coefficient ( 1β ), the second-order AR coefficient ( 2β ) and the direct effect of winter climate

conditions ( 1ω ). This model was similar to Tveraa et al.’s (2007) ‘baseline model’ fitted to 58

populations of semi-domestic reindeer covering a large climatic gradient with large contrasts in

management regimes and vegetation characteristics.

Plotting and interpretation of results

Plotting of results (Figure 4-8) with respect to the interaction between and ( )E dev. st. E were

performed using the vis.gam function [plot i shows both environmental predictors for average

density ( D )], whereas plotting of D (plot ii shows the effect of D for the average values for

both environmental predictors) (see Wood 2008 for details).


RESULTS

Reproductive strategies

Dynamic stated dependent reproductive strategies (DSDS) were superior to fixed strategies (FS) for all

environmental conditions, but the selected DSDS varied among different environments. Higher

degree of environmental stochasticity (using the theoretic input value, y ) resulted in more risk

averse reproductive strategies for all environmental averages ( ; Figure 3a). This relationship was,

however, weakest for improved environmental conditions so we conclude that reindeer

experiencing generally good environments were less risk sensitive compared to individuals

experiencing control and poor conditions. In addition, reindeer experiencing good environments

adopted a risk averse strategy relative to the other environmental averages even for low

environmental stochasticity. A similar conclusion was reached when estimated average female

reproductive allocation (

x

R ) was predicted as a function of environmental stochasticity

[ ] and environmental average (( )E dev. st. E ): (i) improved E and increased both had

negative effects on

( )E dev. st.

R (Figure 4,i); and (ii) increased population density ( D ) had a negative effect

on R (Figure 4,ii). Given the optimal reproductive strategy winning in each simulation, we

investigated how measures of population averages were related to winter weather conditions

[both and ( )E dev. st. E ], and population spring density ( D ). Figure 5 shows that D was

negatively related to both and ( )E dev. st. E .

Reproductive investment

Frequently used empirical measures of reproduction include; (i) the number of offspring per

female (on scale; hereafter termed reproductive success), (ii) autumn and (iii) spring offspring

body mass (used in our previous studies: Bårdsen et al. in press; Bårdsen et al. 2008; Fauchald et

al. 2004; Tveraa et al. 2003; Paper 3). First, reproductive success was practically unaffected by

elog


environmental stochasticity until a certain threshold was reached; then reproductive success

decreased as increased. This threshold was reached earlier in good vs. poor

environments (Figure 6a,i). For large

( )E dev. st.

E , the effect of ( )E dev. st. was practically unimportant.

Second, the relative strength of E and ( )E dev. st. was generally similar with respect to both

offspring autumn and spring body mass, even though the negative effect of was

stronger in the analysis of spring body mass (Figure 6i,b-c). Third, the negative effect of

( )E dev. st.

E was

stronger compared to the negative effect of environmental stochasticity in all three analysis.

The above relationships must be understood in relation to population density ( D ) as D

was clearly negatively related to environmental stochasticity (Figure 5). Larger D lead to lowered

reproductive success and offspring autumn and spring body mass (Figure 6ii,a-c). This happened

even though higher environmental stochasticity clearly resulted in more risk averse reproductive

strategies (Figure 3a). Moreover, increased values of D , E and ( )E dev. st. resulted in lowered R

(Figure 4). The moderate effects of environmental conditions relative to D may come as a

surprise, but it is due to the fact that D has a clear negative effect on offspring autumn body

mass (eqn. A12), which again will affect both survival and spring body mass (eqns. A16-7). In

sum, when it comes to reproductive allocation both the model and previous empirical findings

must be understood in relation to density more than perhaps environmental conditions as

lowered density dependent (food limitation) may compensate for harsh winter conditions.

Somatic investment

Frequently used empirical measures of parental allocation include (i) expected female age (a proxy

for survival as high age is a consequence of high allocation in survival), (ii) autumn and (iii) spring

female body mass (used in our previous studies: Tveraa et al. 2003, Fauchald et al. 2004, Bårdsen

et al. 2008, Bårdsen et al. in press, Paper 3). First, female age was positively related to


environmental stochasticity and negatively related to environmental average; the highest expected

female age was found in generally poor (high E values) and predictable environments [low

values] (Figure 7a,i). Intermediate levels of ( )E dev. st. ( )E dev. st. had the most profound negative

effect on expected female age, at least in good environments. Second, higher degree of

environmental stochasticity resulted in a higher allocation in own growth during summer (Figure

7b,i). Female autumn body mass was not strongly affected by environmental stochasticity until a

certain threshold was reached; after which body mass increase rapidly as increased.

This threshold value was affected by environmental average as the positive relationships between

autumn body mass and seemed to be linear for high

( )E dev. st.

( )E dev. st. E . Additionally, female autumn

body mass positively related to environmental average (Figure 7b,i). Third, for female spring

body mass we also found a positive effect of environmental stochasticity, which also seemed to

be stronger after reaching a threshold value (Figure 7c,i). We did find a rather strong negative

effect for E , which was the opposite as that found for autumn body mass as generally good

conditions (negative E ) gave the highest spring body mass for a given . ( )E dev. st.

The relationships involving female body mass may, as in the analysis of reproductive

allocation, was more or less confounded with populating density ( D ). Large D , however,

resulted in increased expected age (Figure 7a,ii), which means that increased food competition

leads to increased allocation in own survival (see also Figure 4a,ii). Larger D also had a statistical

significantly negative effect on female autumn body mass (Figure 7b,ii), but not on spring body

mass (Figure 7c,ii). In sum, we conclude that a worsening of the environment, i.e. increased D

and/or worsened climate, leads to reduced reproductive allocation at the expense of higher

allocation survival.


Population dynamics

The above analyses prove that worsened environmental conditions have negative effects on the

amount of resources a female invest in reproduction. Such a change in the life history has

important effects on the observed population dynamics. First, we found the strongest direct

negative density dependence ( 1β ) in good and predictable environments; i.e. at low E and

(Figure 8a,i). Not surprisingly, ( )E dev. st. D did have a negative effect on 1β suggesting that

higher density resulted in a stronger direct regulation of populations (Figure 8a,ii). Second, in the

analysis of delayed density dependence ( 2β ) we found that the effect of and ( )E dev. st. E was

purely additive: increased E , decreased ( )E dev. st. and increased D resulted in increased delayed

regulation, but neither effects were statistically significant (Figure 8b). Third, in the analysis of

direct effect of environmental conditions ( 1ω ), the largest negative effect of environmental

conditions was present in good environments (Figure 8c,i). This negative environmental effect

decreased until a threshold was achieved, after this threshold the relationship flattened (Figure

8c,i). Moreover, increased D resulted in a higher impact of 1ω on population growth rates

(Figure 8c,ii). In sum, we conclude that for direct density dependence and the effect of climate

were important limitation in generally poor environments and for high density, but that neither

was important in poor environments.

DISCUSSION

This study shows that climate has large effects on the amount of resources that virtual reindeer

should invest in reproduction vs. survival, which has significant effects on population vital rates

and dynamics. First, DSDS were superior compared to FS in all simulations; FS strategies always

went extinct, which shows that plastic strategies are needed in order to buffer adverse climate.

Second, female reindeer was risk sensitive because more risk averse reproductive strategies did win in


the evolutionary game in harsh, i.e. unpredictable and poor, winter environments compared to

benign, i.e. good and predictable, environments. Third, populations inhabiting benign winter

conditions were the most sensitive to climatic perturbations. This was a result of population

density, which was highest in benign conditions, rather than environmental conditions. Negative

density dependence had a clear negative effect on reproduction relative to the minor impacts of

winter climate. Fourth, populations inhabiting harsh environments were least sensitive to climatic

perturbations. In these environments we found the largest individuals, which were due to the

combined effect low reproductive allocation and low density. Low density lead to a higher reward

for a fixed allocation compared to high density; too high density will, thus, limit the possibility for

individual’s to buffer climate through increased body condition. Harsh winters, thus, act as a

substitute for harvest and predation, due to its lowering of survival, leading to low density. Fifth,

increased density caused increased negative impacts of occasional harsh winters and increased the

strength of direct regulation of populations.

Modelling philosophy and assumptions

All studies using simulation models have to trade complexity over generality, where numerous

books stress the importance of keeping things as simple as possible without loosing too much

realism (e.g. Kokko 2007). This is also the case for our IBM, which is based on numerous

assumptions and simplifications. In this section we will not discuss the shape of relationships and

the parameters used in each sub-model as this is discussed in A1. First, we have a clearly seasonal

model where environmental conditions and population density only have effects during the

winter and summer season respectively. Several studies have shown that an interaction between

winter climate and density have important effects on population dynamics through their joint

effects on adult and juvenile survival (e.g. Grenfell et al. 1998, Coulson et al. 2000). Such

interactions were, however, not built in any of the sub-models in the present IBM. Nevertheless,


rather complex relationship between summer density and winter climate was present in the

statistical models fitted to our output data. The separation of climate and density across seasons

can be viewed as a technical issue; including density dependence in both seasons will only

increase the interaction between them. This would result in an increased impact of climate in

good environments as density would have affected individuals negatively in two seasons instead

of just one. Moreover, empirical evidence on Fennoscandian reindeer indicate that density

dependence has a negative effect on summer pastures (e.g. Bråthen et al. 2007) and on body mass

gain trough the summer but not winter (Paper 3). In contrast, winter climatic conditions have

important effects on body mass gain in late winter, but this effect disappears at some point

during spring and early summer (Fauchald et al. 2004, Bårdsen et al. 2008). The latter results

indicate that, with the exception of perhaps extreme winters, individuals do not carry on lagged

effects of winter climate when they start to breed in the start of the summer season.

Second, important assumptions and simplifications were also undertaken in how the

different reproductive strategies were defined. Real organisms have a much wider behavioral

repertoire than the behavioral rules built into our strategies. Individuals who followed a DSDS

were, for example, assumed to: (i) give birth to a single offspring every year (after reaching prime-

age), all newborns had a constant birth body mass; (ii) have a static reproductive allocation

relative to their age, (iii) not the change their allocation during a given summer; and (iv) they all

had a constant spring body mass threshold deciding whether to invest in reproduction at all.

Numerous studies show that reproductive allocation strategies among female reindeer are not

that simple (e.g. Kojola 1993, Adams 2005, Bårdsen et al. 2008, Bårdsen et al. in press), but

perhaps the most important limitation for our study is the complete lack of evolution as no

strategy changed over time by genetic recombination (as e.g. the IBM by Proaktor et al. 2007).


Reproductive investment

DSDS were superior compared to FS in all simulations. This shows that following a relatively

simple strategy can be sufficient to survive even in rather harsh environments. The FS strategies

always went extinct, which shows that a too simple strategy did not buffer environmental

conditions sufficiently. A higher degree of environmental stochasticity resulted in more risk

averse reproductive strategies for all environmental averages. Moreover, reproductive allocation was

negatively related to environmental average and stochasticity as well as population density.

Reproductive output, i.e. success and offspring body mass, was also negatively related to

environmental average and stochasticity as well as population density. As reproductive allocation

occurs during summer it may not come as a surprise that population density was of greater

importance compared to winter climate. Moreover, population density was low in generally harsh,

i.e. unpredictable and poor, environments (which is a general finding: e.g. Morris and Doak

2002). Consequently, the weak effect that environmental unpredictability had on reproductive

output, which was not predicted, was an artefact of density. Finally, in good environments for a

given environmental stochasticity, average offspring spring body mass was higher than autumn

body mass. This showed that a selection for larger offspring occurred in these environments.

For populations with low harvesting intensities, a higher offspring body mass was found

in poor compared to good winter climate conditions (Tveraa et al. 2007). Even though Tveraa et

al. do not have a clear explanation for this, this fits well with our model as populations

experiencing poor environments in their study were also the ones characterized by low and stable

densities. The interaction between winter climate and density in the present model, i.e. the

combined effect of increased summer gain at low density and the selection for larger offspring

body mass in harsh environments, may thus provide an explanation for the findings by Tveraa et

al. (2007). This, however, contradicts previous experimental studies on Fennoscandian reindeer

where it has been showed that: (1) when females experience a sudden decrease in winter

conditions they promptly reduced their reproductive allocation the following summer; and (2)


when winter conditions were improved, females were reluctant to change their allocation

(Bårdsen et al. 2008). This asymmetric response to improved vs. reduced winter conditions is

consistent with a risk averse reproductive strategy. Similar findings has been found for Alaskan

caribou8 who restrains their reproductive allocation during severe winters (Adams 2005): females,

thus, conserve resources that can be used to either enhance own survival or that can be invested

in an offspring if it survives predation beyond a couple of weeks. Additionally, female reindeer

also invest less in reproduction when population density increases (Paper 3).

Somatic investment

Pseudo-empirical measures of survival and somatic growth were clearly sensitive to

environmental unpredictability; females became more risk averse in more stochastic

environments as both autumn and spring female body mass increased when winter climatic

conditions became more unpredictable. Moreover, increased environmental average had positive

effect on autumn body mass, but affected female spring body mass negatively. The relationship

between density and body mass was much weaker for females compared to offspring. These

findings were expected as: (1) environmental conditions have a direct negative effect on winter

body mass development; (2) density has a direct negative effect on summer body mass

development; and (3) female survival was insensitive to environmental conditions compared to

offspring survival (see A1). As described earlier, reproductive allocation is generally lower in poor

and unpredictable environment and during high population density for many long-lived mammals

including reindeer. Moreover, allocating resources to reproduction is inversely related to

allocation of resources in survival. Our results that a worsening of winter climatic conditions and

increased population density lead to more risk averse reproductive investment with consequent

8 Rangifer sp. generally produce small offspring compared to other closely related species (Adams 2005).


increased allocation in own survival relative to reproduction was, thus, in accordance empirical

evidence from the literature.

Population dynamics

Both environmental unpredictability and average did have important consequences on the

observed population dynamics. Benign environments resulted in the highest density, the highest

level of direct regulation and the most apparent negative effects of climatic on population growth

rates. Mortality rates, especially for juveniles, are high during extreme winters (Tveraa et al. 2003):

populations are, thus, released from negative density-dependence after extreme winters (Aanes et

al. 2000). This implies that harsh winters function similar to harvest in relaxing negative density

dependence in populations inhabiting benign environments. Our findings was similar to Tveraa

et al. (2007) who found that an interaction between density dependence, harvest and climate was

affecting population dynamics. Their main findings was that populations with low harvest-

intensity living in good environments where the most sensitive to climatic perturbations due to

their lack of direct regulation. This was confirmed in our model as we found an interaction

between density and climate where high-density populations experiencing benign winter

environments where the most sensitive to climate.

Conclusions and future prospects

Our IBM proves that plastic life histories may buffer adverse climatic effects and illustrate how

climate interacts with life histories in shaping population dynamics. Future global climate change

will most likely result in a shift towards more frequent extreme precipitation events (e.g. Wilby

and Wigley 2002, Semmler and Jacob 2004, Tebaldi et al. 2006, Benestad 2007, Sun et al. 2007), a

trend that is already empirically evident on several continents (Sun et al. 2007 and references

therein). Moreover, many of these climatic scenarios are expected to happen both sooner and


more pronounced in the northern hemisphere (e.g. Tebaldi et al. 2006, Benestad 2007). Rangifer,

which is a northern and circumpolar species, and the northern ecosystems they inhabit, thus,

represent suitable modeling systems for assessing impacts of future climate change. Hanssen-

Bauer et al. (2005), for example, review several studies predicting how climate will change in

Fennoscandia in the future: (i) increased warming rates with distance to the coast, (ii) higher

warming rates in winter compared to summer, and (iii) increased precipitation especially during

winter. The shifts between warm and cold periods during winter coupled with an year-round

increased intensity of precipitation (Hanssen-Bauer et al. 2005), will lead to an increased

frequency of wet weather, deep snow and ice crust formation that has negative consequences for

large herbivores (e.g. Solberg et al. 2001).

The present model do not, however, include an increased frequency and intensity of precipitation

events as we have solely used normally distributed environmental conditions, but this can easily

be implemented in the future by using other distributions such as e.g. the skew-normal

distribution (Azzalini 2005). Another issue with regard to how climate was implemented in the

present model was that we did not included any of the above mentioned weather phenomena

(e.g. precipitation and icing events) as we simulated climate using an index. We do not, however,

see this as a problem as important climatic events like the ones described above gives clear

signatures in existing climatic indexes such as e.g. the NAO (reviewed by e.g. Ottersen et al. 2001,

Stenseth et al. 2002, Hurrell et al. 2003). In spite of this, not all predicted changes are believed to

have negative effects, which was the rationale for implementing both ‘improved’ and ‘reduced’

environmental averages. If we use semi-domestic reindeer in Europe as an example, herding

practices along with pasture quality (e.g. an earlier and longer growing season) combined with

climate change are predicted to affect the husbandry negatively in Scandinavia, neutral in Finland

and positive in Russia (Rees et al. 2008). Even if the future brings improved average climatic

conditions compared to the present situation, almost all climate models predicts future winter


climatic conditions to be more stochastic than present day for most of the areas inhabited by

reindeer. If this prediction is correct, the results from the IBM combined with our previous

studies show that such an unpredictable climate will result in reindeer adopting more risk averse

reproductive investment strategies (even for improved environments). This, along with the potential for

buffering harsh winters through reduced reproductive allocation, will again have dramatic

negative effects on both population abundance and reproduction.

The ability for individual’s to buffer negative climatic effects through plastic life histories have

important consequences on how the impacts of future climate change must be understood. For

example, many recent analyses of climatic effect signatures in population time series have been

used to infer the likely consequences of future climate change (Stenseth et al. 2002). The

predicted consequences commonly invoke more frequent population collapses (e.g. Post 2005).

Such inferences are based on an underlying assumption that animals have non-plastic life history

strategies that are not adequately adaptive to new climate regimes. Contrary to recent studies,

such as e.g. the one by Post (2005), our model combined with empirical findings suggest that

these changes will more likely results in more risk averse life histories that have the potential of

buffering negative effects of climate up to a certain point. We, thus, propose that future studies

should focus more on how long-lived organisms, such as large terrestrial herbivores, adjust their

life history to counteract climate changes.

Acknowledgments.-- The present study was funded by the Research Council of Norway. We thank

Nigel G. Yoccoz, Marius W. Næss, Øystein Varpe, Knut Langeland, Kjell E. Erikstad and Børge

Moe for comments and discussions that have greatly improved the manuscript. We thank Heikki

Törmänen for providing us with unpublished results, and Geir W. Gabrielsen helped us with

some physiological calculations.


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Figure 1. A schematic diagram of the individual-based model of optimal reproductive strategies

and population dynamics for a temperate large-herbivore. Grey lines indicate scheduling. And all

simulations are started with the same initial conditions. Detailed description of the diagram: (i)

Individual-level processes (rectangles) represented by females spring ( ) and autumn body

masses ( ), investment strategy ( and which again influence the gain), summer

metabolic rate ( ) and proportional winter mass loss ( ). (ii) Population-level processes (circles)

represented by summer population density ( ) and winter environmental conditions ( ).

tjibmSpring,,

tjibmAutumn,,

iS ,β

jiR , jiS ,

tj , tjiW ,,β

tD tE

Figure 2. Cost of reproduction, evaluated over a one year time step, for female reindeer with

constant spring body mass of 60.7 kg for three different population densities (D = 1.25, 3.25 &

5.25 individuals km-2) and winter environmental conditions (E = -1.5, 0.0 & 1.5). Note that

offspring survival is conditional on an individual being a female so actual survival probability in

the model is the above estimates multiplied with 0.5 (assuming a constant 1:1 birth sex ratio).

Figure 3. The winning strategy and the design with respect to environmental conditions (a), and

the theoretic relationship between female reproductive investment ( ) as a function of spring

body mass for dynamic state dependent reproductive strategies (b). The relationship between reproductive

investment and spring body mass ( in eqn. 4) is different across strategies. Individuals will not

invest in reproduction if their spring body mass is below a threshold value (

R

Rb

springτ ). The thick grey

arrow (a) shows the risk-averse risk-prone continuum, whereas dotted blue lines shows the range in

R-values for different female spring body massed for each winning strategy (25-30). Note that the

two most risk averse strategies (a; 25-6), is present as the two points with the lowest average

female reproductive investment ( R ) in all subsequent figures. In some figures (subplot i in Figure

5,6 & 7a) these two points ‘force’ a curved model to be fitted to the data. If these points are

removed more straight line relationships would have occurred. Deviance explained (D) by the

model are given in percentage.


Figure 4. GAM model showing that average female reproductive investment ( R ) was a function

of smoothen (s) interaction between standard deviation [ ( )E dev. st. ] and average ( E )

environmental conditions and population density ( D ): Intercept = 0.335 (st. err = 0.001, P <

0.001), (i) estimated degrees of freedom for s[ ( ) st. E dev. , E ] = 2.651 (P < 0.001), and (ii) s( D ) =

2.667 (P < 0.001). Deviance explained (D) by the model are given in percentage.

Figure 5. GAM model showing average population density ( D ) as a function of the smoothen (s)

interaction between standard deviation [ ( )E dev. st. ] and average ( E ) environmental conditions:

Intercept = -1.680 (st. err = 0.075, P < 0.001), (i) estimated degrees of freedom for s[ ( )E dev. st. ,

E ] = 7.239 (P < 0.001). Deviance explained (D) by the model is given as a percentage in the plot.

Figure 6. GAM model showing reproductive investment as a function of the smoothen (s)

interaction between standard deviation [ ( )E dev. st. ] and average ( E ) environmental conditions as

well as average population density ( D ): (a) Number of offspring per female (on scale);

Intercept = -1.584 (st. err = 0.010, P < 0.001), (i) estimated degrees of freedom for s[

elog

( )E dev. st. ,

E ] = 8.972 (P < 0.001), and (ii) s( D ) = 2.992 (P < 0.001). (b) Offspring autumn body mass;

Intercept = 36.083 (st. err = 0.070, P < 0.001), (i) estimated degrees of freedom for s[ ( ) st. E dev. ,

E ] = 7.911 (P < 0.001), and (ii) s( D ) = 2. 931 (P < 0.001). (c) Offspring spring body mass;

Intercept = 38.010 (st. err = 0.137, P < 0.001), (i) estimated degrees of freedom for s[ ( ) st. E dev. ,

E ] = 9.689 (P < 0.001), and (ii) s( D ) = 2.912 (P < 0.001). Deviance explained (D) by the model

are given as percentages on each plot.


Figure 7. GAM model showing somatic investment as a function of the smoothen (s) interaction

between standard deviation [ ] and average (( )E dev. st. E ) environmental conditions as well as

average population density ( D ): (a) Female age; Intercept = 8.337 (st. err = 0.019, P < 0.001), (i)

estimated degrees of freedom for s[ ( )E dev. st. , E ] = 9.433 (P < 0.001), and (ii) s( D ) = 3.000 (P <

0.001). (b) Female autumn body mass; Intercept = 93.948 (st. err = 0.134, P < 0.001), (i)

estimated degrees of freedom for s[ ( )E dev. st. , E ] = 6.115 (P < 0.001), and (ii) s( D ) = 1.000 (P =

0.017). (c) Female spring body mass; Intercept = 82.915 (st. err = 0.123, P < 0.001), (i) estimated

degrees of freedom for s[ , (E st. )dev. E ] = 6.927 (P < 0.001), and (ii) s( D ) = 1.000 (P = 0.212).

Deviance explained (D) by the model are given as percentages on each plot.

Figure 8. GAM model showing population dynamics as a function of the smoothen (s)

interaction between standard deviation [ ( )E dev. st. ] and average ( E ) environmental conditions as

well as average population density ( D ): (a) Direct regulation (1 1β− ); Intercept = -0.405 (st. err =

0.014, P < 0.001), (i) estimated degrees of freedom for s[ ( )E dev. st. , E ] = 6.836 (P = 0.040), and

(ii) s( D ) = 1.599 (P = 0.009). (b) Delayed regulation ( 2β ); Intercept = -0.028 (st. err = 0.118, P =

0.119), (i) estimated degrees of freedom for s[ ( )E dev. st. , E ] = 2.000 (P = 0.109), and (ii) s( D ) =

1.767 (P = 0.231). (c) Direct effect of environmental conditions ( 1ω ); Intercept = -0.111 (st. err =

0.004, P < 0.001), (i) estimated degrees of freedom for s[ ( )E dev. st. , E ] = 4.227 (P = 0.033), and

(ii) s( D ) = 2.251 (P = 0.011). Deviance explained (D) by the model are given as percentages on

each plot.


Initiation (t = t0 )

An initial spring population is generated with aStable age-structure (j = 2) Normally distributed spring body mass

Equal across strategiesIndividuals (i) with different investment strategies

Reproductive investment Ri,j = [0,1]Investment in soma/survival Si,j = 1 – Ri,jTotal energy investment Toti,j = Ri,j + Si,j = 1

÷÷

Autum

n (t)

Assess if above reproductive threshold

Update mother/offspring parameters and population density

no

Assess winter survival

no

Update body mass

÷÷

÷÷ ÷÷

yes

Spring (t+1)

+ +

Spring (t)

++

÷

÷

+

+

+ yes

+

++

tjibmSpring

,, tjibmBirth

,,

tjibmAutumn

,1, ≥ tjibmAutumn

,1, <

tD

tjiS ,,β

tEtjiW ,,β

jiS , jiR ,

÷

tjiGain ,1, <tjiGain ,1, ≥

Summ

erW

inter

Figure 1.


0.2

0.4

0.6

0.8

1.0(a)

Dens i t y

E = -1.5

0.25

1.75

3.25

Spring body mass = 60.7 (kg)

0.0

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

1.0(b) E = 0

0.0

0.2

0.4

0.6

0.8

0.0

0.2

0.4

0.6

0.8

P(o

ffspr

ing

surv

ival

| fe

mal

e)

0.2

0.4

0.6

0.8

1.0(c) E = 1.5

0.0 0.2 0.4 0.6 0.8 1.0

P(fe

mal

e su

rviv

al)

R

Figure 2.


25

26

27

28

29

30

0.0 0.5 1.0 1.5

(a) Reproductive strategy (D = 73.28%)St

rate

gy

Theoretical envionmental average, x

Control

Improved

Reduced

Riskaverse

Riskprone

Theoretical envionmental stochasticity, y

0.0

0.2

0.4

0.6

0.8

1.0

R

(b) Reproductive investment (R) Strategy

50 70 90 110

25

26

27282930

Female spring body mass (kg)

Figure 3.


-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

(i)

Environmental stochasticity [st. dev. (E )]

Envi

ronm

enta

l ave

rage

( E)

0.0 0.5 1.0 1.5

(a) Reproductive investment (R )

D = 53.35%

0.30

0.32

0.34

0.36

(ii)

loge[density (D )]

R

-4 -3 -2 -1

Figure 4.


0.0 0.5 1.0 1.5

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3


Env

ironm

enta

l ave

rage

(E)

(a) loge[d ensi ty ( km−2)]

D = 64.47%

Figure 5.


-0.3

-0.2-0.1

0.00.1

0.2

0.3

(i)(a) loge(Nof f spring/N female)

D = 99.16%

-2

-1

0

1

2

(ii)

log e

(Nof

f/Nfe

m)

-0.3

-0.2-0.1

0.00.1

0.2

0.3

Envi

ronm

enta

l ave

rage

( E)

(b) Offspring autumn body mass (kg)

D = 88.23%

34

36

38

40

42

44

Body

mas

s

0.0 0.5 1.0 1.5

-0.3

-0.2-0.1

0.00.1

0.2

0.3

Environmental stochasticity [st. dev. (E)]

(c) Offspring spring body mass (kg)

D = 89.28%

35

40

45

50

55

loge[density (D )]

Body

mas

s

-4 -3 -2 -1

Figure 6.


-0.3

-0.2-0.1

0.00.1

0.2

0.3

(i)(a) Female age (year)

D = 81.1%

7.5

8.0

8.5

9.0

(ii)

Fem

ale

age

-0.3

-0.2-0.1

0.00.1

0.2

0.3

Envi

ronm

enta

l ave

rage

( E)

(b) Female autumn body mass (kg)

D = 59.09%

88

90

92

94

96

98

Body

mas

s

0.0 0.5 1.0 1.5

-0.3

-0.2-0.1

0.00.1

0.2

0.3

Environmental stochasticity [st. dev. (E)]

(c) Female spring body mass (kg)

D = 60.41%

76788082848688

loge[density (D )]

Body

mas

s

-4 -3 -2 -1

Figure 7.


-0.3-0.2

-0.10.00.1

0.20.3

(i)(a) Direct regulation (β1)

D = 45.02%

-0.6

-0.4

-0.2

0.0

(ii)

β 1

-0.3-0.2

-0.10.0

0.10.2

0.3

Envi

ronm

enta

l ave

rage

( E)

(b) Delayed regulation (β2)

D = 6.89%

-0.4

-0.2

0.0

0.2

0.4

β 2

0.5 1.0 1.5

-0.3

-0.2

-0.1

0.00.1

0.20.3


(c) Environmental conditions (ω1)

D = 25.92%

-0.20

-0.15

-0.10

-0.05

0.00

0.05

loge[density (D )]

ω1

-4 -3 -2 -1

Figure 8.

Plastic reproductive allocation and environmental unpredictability A1.1

A1: SPECIFICATION – FORMULATING AN INDIVIDUAL-

BASED MODEL (IBM)

This document follows a modified version of the Overview, Design concepts and Details (ODD)

protocol for IBMs (Grimm and Railsback 2005, Grimm et al. 2006).

I. OVERVIEW

1. PURPOSE

How life history trade-offs are related to environmental stochasticity is poorly understood.

However, recent studies suggest a strong impact of winter severity on the cost of reproduction in

large herbivores (Clutton-Brock and Pemberton 2004). When reproduction competes with the

amount of resources available for survival during an unpredictable non-breeding season,

individuals should adopt a risk sensitive regulation of their reproductive allocation (Bårdsen et al.

2008). Temperate large-herbivores face such a trade-off as reproductive allocation competes with

acquisition and maintenance of body reserves during summer. For these animals autumn body

mass functions as an insurance against stochastic winter climatic severity (Reimers 1972,

Skogland 1985, Clutton-Brock et al. 1996, Tveraa et al. 2003, Fauchald et al. 2004). Thus,

reproductive allocation during summer should depend on the expected winter conditions (e.g.

Tveraa et al. 2007, Bårdsen et al. 2008). As a follow-up to our own empirical studies on reindeer

Rangifer tarandus (Tveraa et al. 2003, Fauchald et al. 2007, Tveraa et al. 2007, Bårdsen et al. 2008)

we will investigate how environmental conditions affect optimal reproductive allocation

strategies, and to what extent reproductive allocation strategies affect population dynamics.

Individuals living in a highly unpredictable environment should be on the risk averse side of a

risk prone-risk averse continuum (see Bårdsen et al. 2008). For a given distribution of winter

conditions, a risk prone reproductive strategy involves high reproductive allocation that will result in

high reproductive reward during benign winters but high survival cost during harsh winters. A

low reproductive allocation will, on the other hand, result in stable winter survival but lower

potential reproductive reward. Consequently, this represents a risk averse reproductive strategy. Risk


averse reproductive strategies are believed to result in more stable population dynamic, i.e. more or less

constant population density, as the individuals buffer their reproductive allocations against a

harsh environment. The objective of this study is to develop an IBM that will give us answers to

the following research questions:

(1) How does environmental stochasticity affect the optimal reproductive allocation strategy?

(2) How do different reproductive allocation strategies affect population dynamics?

2. STATE VARIABLES AND SCALES

This model consists of three main components and the interaction between them.

Low-level state variables (individual specific states):

(1) Individual state variables: age ( j ; year) and body mass (kg); assumed known by the

individuals.

High-level state variables (population specific states):

(2) Summer density: the number of individuals ( tn ) per km2 present during the summer season

( tD ); assumed known by the individuals.

(3) Winter (weather) conditions: environmental stochasticity (the distribution of winter climatic

conditions which may be defined by a distribution’s mean, variance and skew). The

distribution is assumed known by the individuals whereas its value within each time step

( tE ) is not (individuals cannot ‘look into the future’).

3. PROCESS OVERVIEW AND SCHEDULING

Time ( t ) is discrete (one step equals one year) with two distinct seasons (summer and winter) per

time step. The model will be run for T time steps, i.e. from spring at 0tt = to autumn at

. A key point is that individuals are not assumed to know future winter conditions but

they have an ‘estimate’ of the distribution of this variable. Thus, even though a process that

affects individual parameters in one season will have effects in coming seasons (e.g. summer

allocation and winter survival) it is crucial that these processes are treated independent over

seasons in the model. A schematic overview of processes and scheduling are presented in Figure

T+tt = 0


A1.1, but below are a verbal presentation of the processes separated by season (summer &

winter).

Summer (1 May to 31 October; 184 days).-- An allocation strategy will in any point in time be a

scalar representing an individual’s allocation of resources (spring body mass) in

reproduction vs. somatic growth (a proxy for survival) during summer. An individual can

only invest in reproduction ( ) and survival ( ); i.e. R S 1=+ SR

6.0

. The reward for a fixed

allocation will be limited by the population’s summer density ( ). That is, an individual

with a fixed reproductive allocation strategy, e.g.

D

=R , will collect a higher mean

reproductive reward in low- vs. high-density years. The effect of allocation in reproduction

and survival will be implemented in two functions (Figure A11): (1) one gain function for

females ( where and are predictors) and (2) one function for offspring (where

and are predictors). In sum, individual autumn body mass, i.e. summer mass

development, depends on: (1) spring body mass (in the first year of life this will be an

individual’s birth mass), (2) the gain function that represents the increase in body mass per

kg spring mass, and (3) a basal summer metabolic rate (

Gain S D R

D

Sβ ).

Winter (1 November to 31 April; 181 days).-- Autumn body mass is a predictor for the three

processes that happens in the autumn and during winter: (1) If offspring body mass is

below a threshold ( autumnτ ) it will be removed from further analyses (to ease the

implementation of the model, winter survival of offspring with body masses below autumnτ

will be set to zero even though the biological rationale for this is that offspring with such a

low mass will die during summer). (2) Autumn mass and winter conditions ( ) will be a

predictor of individual winter survival probability ( ). (3) If an individual survives, its

body mass next spring will depend on its autumn mass as well as a winter loss of body mass

(

E

SurvivalP

Wβ ). After these processes have been run time will go one step forward (from t to 1+t )

and the following parameters will be updated; (1) mortality, (2) spring body mass, (3) age

and (4) population density.


II. DESIGN CONCEPTS

4. DESIGN CONCEPTS

This part of the ODD is based on concepts described in detail in Grimm and Railsback (2005:

chapter 5).

Emergence.-- Population dynamics emerge from the behaviour of individuals. However, individual

behaviour is linked to empirical rules. This can be illustrated by the following example:

individual autumn body mass is based on spring mass, a built-in allocation strategy (within

the limits set by population density) and basal summer metabolic rate.

Adaptation.-- In addition to the individual specific state variables individuals have an built-in

strategy, which defines a behavioural rule to follow. Two types of strategies are tested

against each other in the present study. First, a fixed strategy is defines by a vector looking

like e.g. , which means that this individual will invest zero in

reproduction its first year of life, and 0.4 for the rest of its life (this example shows an

individual that reaches a maximum age, , of 5 years). Second, a dynamic state dependent

strategy reproductive allocations will in this model depend on spring body mass (state),

looking like e.g. (see below).

[ 0.4 0.4, 0.4, 0.4, 0.0,=iR

0.7, 0.4, 0.0,=iR

]

maxj

[ ] 0.0,0.4

Sensing.-- Within each season, individuals are assumed to know their body mass, age, summer

population density and winter environmental condition.

Fitness.-- Fitness, i.e. the long-term performance of alleles and strategies of traits (Coulson et al.

2006 and references therein), will be assessed in this IBM. When evaluating fitness over

different strategies, one can say that ‘an optimal strategy maximizes the expected number of

decedents left far into the future’ (e.g. McNamara and Houston 1996, McNamara 1997,

2000). For each scenario (different environments) the model will be run for as many time

steps ( ) necessarily for the model to converge (see e.g. Proaktor et al. 2007). In the end of

a simulation we will have a time series that consists of e.g. the proportion of individuals

applying the different strategies, population density and winter conditions. This makes it

possible to follow strategies over time.

T


Prediction.-- Individuals cannot foresee the future. This is the main reason for modelling processes

over two distinct seasons.

Interaction.-- Individuals interact indirectly through a shared food resource. This is implemented as

the negative density dependence acting on body mass development throughout summer in

the gain function. The only positive interaction between individuals is the positive effect of

a mother’s reproductive allocation on her offspring’s autumn body mass.

Stochasticity.-- Winter conditions are drawn from a normal or skew-normal distribution. The

empirical distribution, i.e. the actual vectors generated and used in the simulations, is varied

by changing important distributional parameters (see INPUT section below for details).

Observation.-- Book keeping consists of recording a set of variables per time step.

Low-level state variables (individual-specific):

(1) Body mass of both females and offspring in spring and autumn.

(2) Survival (including survival probability) of both females and offspring.

High-level state variables (population-specific):

(3) The number and proportion of individuals with different allocation strategies.

(4) Summer density.

(5) Winter weather conditions.

III. DETAILS

5. INITIATION & CONVERGENCE

The model will be initiated by creating ( ) animals with body masses generated from a normal

distribution with a stable age distribution ( year). Moreover, each individual will be

provided with different reproductive allocation strategies. The number of different strategies

( ) give rise to

0tn

20=tj

stratn stratt nn0

number of individuals ‘playing’ the same strategy. The number of

individuals following each strategy and the distribution of body mass will be equal for all

allocation strategies irrespectively of the type of strategy. Table A1.1 provides details on initiating

the IBM.


A simulation is said to converge when one winning strategy is left alone. After this happened, we

ran the simulation for 20 more years as to ‘harmonize’ the dynamic between the individuals in the

population and environmental conditions. Then, we collected data on yearly averages on

important output for another 60 years; i.e. ‘pseudo-empirical’ time-series data from 60−=Tt to

Tt = .

6. INPUT

Winter environmental condition ( E ) is drawn from a normal distribution (Figure A1.2). E is the

only variable differing over each simulation. Moreover, the distribution of this variable will be

generated based on a real climate variable; the Arctic Oscillation1 (AO; also known as the

Northern Annular Mode).

7. SUBMODELS

Reproductive investment strategies defined on a continuous scale

Investment in reproduction.-- An individual ( ) of age ( ) and a spring body mass ( ) will at

a given year (

i jtji

bmSpring,,

t ) invest a proportion of its available resources in reproduction ( [ ]1,0,, =tjiR ):

0,1, =≤ tjiR if . (A1) 1≤j

This ensures that juveniles ( ) do not reproduce; they will invest everything in somatic

growth. A fixed strategy is defined as a scalar between 0 and 1 that represents an allocation

rule that an individual will follow throughout its adult life (see Adaptation section above for

an example of ). In a dynamic state dependent strategy reproductive allocation will be

estimated and updated each year according to the following equations:

1≤j

4.0,1, => tjiR

([ ])tjibmRR Springbatjie

R,1,1

1,,

>×+−

+= if & if 1>j springbm tji

Spring τ>< ,1,

(A2)

0=R 1,, tji . if ≤j or if Spring springbm tjiτ≤

< ,1, (A3)

Juveniles ( ) and individuals with a spring body mass below a threshold value (1≤j springτ )

will not invest in reproduction. Consequently, females in poor condition will skip 1 Data and detailed information are freely available: http://www.cgd.ucar.edu/cas/jhurrell/indices.info.html#nam.

http://www.cgd.ucar.edu/cas/jhurrell/indices.info.html#nam


reproduction, or have reproductive pauses (e.g. Reimers 1983b, Cameron 1994), in order

to invest more in their own soma. Since the intercept ( ) in this logistical equation will be

constant for all strategies (Table A1.1), it is the slope ( ) of the relationship between

reproductive allocation and spring body mass ( ) that defines different strategies.

Thus, a dynamic state dependent strategy can in a simplified way be defined as:

Ra

Rb

tjibm ,,Spring

[ ] [ ] RRRRRtji bbbbbRjjjj

≈≈====

,0...,,,0max32,, . (A4)

Individuals with a dynamic state dependent strategy will initially be given different slope values

( ), which will be limited within the range of and (Table A1.1 & Figure A1.4). RbminRb

maxRb

Investment in somatic growth. -- Moreover, allocation in somatic growth, a proxy for survival, is then:

tjitji RS ,,,, 1−= . (A5)

Thus, total energy allocation will sum to one ( 1,, =+ jiji R

1≥j

S ), which means that individuals

either allocate resources to reproduction or survival and nothing else.

Summer processes

Autumn body mass (Figure A1.5a-b).-- Individual ( i ) autumn mass ( ) depends on

age (if an individual will be a juvenile and if it will be defined as an prime-

aged/adult), birth mass ( ) or spring female body mass ( ), the gain in mass

through summer ( ) and a constant basal summer metabolic rate (

0,,≥

tjibmAutumn

tjibmSpring,,

jiS ,

1<j

tibmBirth,

tj,iGain , t,β ) within the

limits set by a threshold body mass (j

bmτ ):

)(tjititji Stjibmbm GainBirthAutumn

,1,,,1, ,1, << tji ,,bmSpring −×+= < β if 1<j (A6)

)(tjitjitji Stjibmbm ,1,,,,1, ,1, ≥≥

β if 1≥j (A7) tjibm ,,

SpringGainSpringAutumn = + −×≥

tjitji bmbm ,,,,AutumnAutumn = if Autumn

jtji bmbm τ<

Autumn

,, (A8)

jtji bmbm τ=,,

if Autumnjtji bmbm τ≥

,,. (A9)

Thus, female autumn mass is a function of how much she invests in somatic growth,

whereas offspring autumn mass is a function of how much its mother invests in


reproduction (Table A1.2a). Basal metabolic rate (tjiS ,,

β ), based on reported estimates from

the literature, was found to be linearly related to body mass (Figure A1.5c; see also Table

A1.2a for details):

( )tjitji bmS Springba

,,,,×+= βββ if 1<j (A10)

)(titji bmS ,,, ββ Birthba ×+=β if 1≥j . (A11)

Gain function (Figure A1.6).-- This function determines the per capita gain in body mass (i.e. ‘per

kilo’ females spring mass) over the summer ( ). Gain depends on an individual’s

allocation strategy, and it is different for juveniles (

0,, ≥tjiGain

1<j ) and adults ( ): 1≥j

)()()( ,,11, tjiGtGjijGtji DRdDcRbGain ×++= << if 1<j (A12)

)()()( DSdDcSbGain ,,1,1, tjiGtGjijGtji ×++= ≥≥ if 1≥j . (A13)

Offspring autumn body mass will thus depend on how much their mothers invest in

reproduction ( ), whereas female autumn mass will depend on how much she invests in

somatic growth ( ) under the constraints that density ( ) represents (Table

A1.2b).

jiR ,

iS jij R ,, 1−= tD

‘Summer survival’ (Figure A1.5a & A1.7a).-- If autumn body mass is below a threshold value

(jautumnτ ) it will be set to zero:

0,,=

tjibmAutumn if jtji autumnbmAutumn τ<

,, (A14)

tjitji bmbm ,,,,AutumnAutumn = if Autumn

jtji autumnbm τ≥,,

. (A15)

The rationale for setting mass to zero is to mimic summer survival. In order to avoid one

loop in the programming code survival is only modelled in the winter season (Table A1.2).

Winter processes

Winter survival (Figure A1.7).-- Individual winter survival conditional of being a female,

( ) [ ]1,0|1,, =+ femaleSurvivalP tji , depends on autumn body mass. We follow the female segment


of the population only so offspring survival probability will be multiplied with 0.5. Survival

is negatively related to environmental conditions ( ) and it follows a logistical form (with

an asymptote of ):

tE

jWI

( )( ) ⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

+

×=⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ ××+×+⎟

⎠⎞

⎜⎝⎛ ×Autumn+−

tjibmtjWtjWtjibmjWjWj

AutumnEdEcbaW

e

IfemaleSurvivalP,,,,1

1|+tji 1,, . (A16)

This function is different for adult females and offspring as discussed in the literature

(Table A1.2c).

Spring body mass (Figure A1.8).-- If an individual survives, its body mass next spring ( ) will

depend on autumn body mass as well as a proportional loss of body reserves during winter

(

1+t

tjiW ,,β ):

( )[ ] ⎭⎬⎫

⎩⎨⎧×Loss

+= +×+− tjitLossLosstji eEbaW

eI

,,,, 11

β if (A17) 11,,=

+tjiSurvivalP

( ) if P . (A18) 1=1,, +tjiSurvivaltjitjitji Wbmbm AutumnSpring

,,,,,1,1 β−×

+ 1=

+

Winter losses increases with increasing environmental conditions ( ), and this relationship

has a logistical form: smaller values the scaling parameter (

tE

Lossϑ ) gives a higher degree of

curvature (highly sigmoid shape) compared to lager values of Lossϑ (see Table A1.2d for

details). The absolute loss of body mass will be larger for large individuals (eqn. A18), but

the proportional loss of body reserves are equal for lager and smaller individuals. Moreover,

we have added individual stochasticity ( ) to winter loss of body mass in order model

chance operating on individual performance during winter (Table A1.2d).

tjie ,,

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Alaskan caribou. Journal of Mammalogy 86:506-513. Albon, S. D., A. Stien, R. J. Irvine, R. Langvatn, E. Ropstad, and O. Halvorsen. 2002. The role of

parasites in the dynamics of a reindeer population. Proceedings of the Royal Society of London Series B-Biological Sciences 269:1625-1632.

Bergerud, A. T. 1974. Decline of caribou in North America following settlement. The Journal of Wildlife Management 38:757-770.


Bradshaw, C. J. A., S. Boutin, and D. M. Hebert. 1998. Energetic implications of disturbance caused by petroleum exploration. Canadian Journal of Zoology 76:1319-1324.

Bårdsen, B.-J., P. Fauchald, T. Tveraa, K. Langeland, N. G. Yoccoz, and R. A. Ims. 2008. Experimental evidence for a risk sensitive life history allocation in a long-lived mammal. Ecology 89:829-837.

Cameron, R. D. 1994. Reproductive pauses by female caribou. Journal of Mammalogy 75:10-13. Clutton-Brock, T. H., and J. M. Pemberton, editors. 2004. Soay Sheep - dynamics and selection in

an island population. Cambrigde University Press, Cambrigde, UK. Clutton-Brock, T. H., I. R. Stevenson, P. Marrow, A. D. MacColl, A. I. Houston, and J. M.

McNamara. 1996. Population fluctuations, reproductive costs and life-history tactics in female Soay sheep. Journal of Animal Ecology 65:675-689.

Coulson, T., T. G. Benton, P. Lundberg, S. R. X. Dall, B. E. Kendall, and J. M. Gaillard. 2006. Estimating individual contributions to population growth: evolutionary fitness in ecological time. Proceedings of the Royal Society B-Biological Sciences 273:547-555.

Crête, M., S. Counturier, B. J. Hearn, and T. E. Chubbs. 1994. Relative contribution of decreased productivity and survival to recent changes in the demographic trend of the Riviere George Caribou Herd. Rangifer Special Issue 9:27-36.

Dauphiné, T. C., Jr. 1976. Biology of the Kaminuriak population of barren-ground caribou. part 4: growth, reproduction and energy reserves. 38, Canadian Wildlife Service.

Fancy, S. G., K. R. Whitten, and D. E. Russell. 1994. Demography of the Porcupine Caribou Herd, 1983-1992. Canadian Journal of Zoology 72:840-846.

Fauchald, P., R. Rødven, B.-J. Bårdsen, K. Langeland, T. Tveraa, N. G. Yoccoz, and R. A. Ims. 2007. Escaping parasitism in the selfish herd: age, size and density-dependent warble fly infestation in reindeer. Oikos 116:491-499.



Grimm, V., U. Berger, F. Bastiansen, S. Eliassen, V. Ginot, J. Giske, J. Goss-Custard, T. Grand, S. K. Heinz, G. Huse, A. Huth, J. U. Jepsen, C. Jørgensen, W. M. Mooij, B. Muller, G. Pe'er, C. Piou, S. F. Railsback, A. M. Robbins, M. M. Robbins, E. Rossmanith, N. Rüger, E. Strand, S. Souissi, R. A. Stillman, R. Vabø, U. Visser, and D. L. DeAngelis. 2006. A standard protocol for describing individual-based and agent-based models. Ecological Modelling 198:115-126.

Grimm, V., and S. F. Railsback. 2005. Individual-based modelling and ecology. Princeton University Press, Princeton, New Jersey, USA.


Holand, O., H. Gjøstein, A. Losvar, J. Kumpula, M. E. Smith, K. H. Røed, M. Nieminen, and R. B. Weladji. 2004. Social rank in female reindeer (Rangifer tarandus): effects of body mass, antler size and age. Journal of Zoology 263:365-372.

McNamara, J. M. 1997. Optimal life histories for structured populations in fluctuating environments. Theoretical Population Biology 51:94-108.

McNamara, J. M. 2000. A classification of dynamic optimization problems in fluctuating environments. Evolutionary Ecology Research 2:457-471.

McNamara, J. M., and A. I. Houston. 1996. State-dependent life histories. Nature 380:215-221. Nilssen, K. J., J. A. Sundsfjord, and A. S. Blix. 1984. Regulation of metabolic rate in Svalbard and

Norwegian reindeer. American Journal of Physiology - Regulatory, Integrative and Comparative Physiology 247:R837-R841.

R Development Core 2007. R: a language and environment for statistical computing. R version 2.6.0. R Foundation for Statistical Computing, Vienna, Austria. www.R-project.org.

Proaktor, G., T. Coulson, and E. J. Milner-Gulland. 2007. Evolutionary responses to harvesting in ungulates. Journal of Animal Ecology 76:669-678.


Reimers, E. 1983a. Growth rate and body size differences in Rangifer, a study of causes and effects. Rangifer 3:3-15.

Reimers, E. 1983b. Reproduction in wild reindeer in Norway. Canadian Journal of Zoology 61:211-217.

Rødven, R. 2003. Tetthet, klima, alder og livshistorie i en tammreinflokk i Finnmark. University of Tromsø, Tromsø, Norway. [in Norwegian]

Schmidt-Nielsen, K. 1997. Animal physiology: adaptation and environment, Fifth edition edition. Cambridge university press, Cambridge, United Kingdom.

Skogland, T. 1985. The effects of density-dependent resource limitations on the demography of wild reindeer. Journal of Animal Ecology 54:359-374.



Valkenburg, P., R. W. Tobey, B. W. Dale, B. D. Scotton, and J. M. Ver Hoef. 2003. Body size of female calves and natality rates of known-aged females in two adjacent Alaskan caribou herds, and implications for management. Rangifer Special Issue 14:203-209.


Initiation (t = t0 )

An initial spring population is generated with aStable age-structure (j = 2) Normally distributed spring body mass

Equal across strategiesIndividuals (i) with different investment strategies

Reproductive investment Ri,j = [0,1]Investment in soma/survival Si,j = 1 – Ri,jTotal energy investment Toti,j = Ri,j + Si,j = 1

÷÷

Autum

n (t)

Assess if above reproductive threshold

Update mother/offspring parameters and population density

no

Assess winter survival

no

Update body mass

÷÷

÷÷ ÷÷

yesSpring (t+

1)

+ +

Spring (t)

++

÷

÷

+

+

+ yes

+

++

tjibmSpring

,, tjibmBirth

,,

tjibmAutumn

,1, ≥ tjibmAutumn

,1, <

tD

tjiS ,,β

tEtjiW ,,β

jiS , jiR ,

÷

tjiGain ,1, <tjiGain ,1, ≥

Summ

erW

inter

Figure A1.1. A schematic diagram of the individual-based model of optimal reproductive strategies

and population dynamics for a temperate large-herbivore. Grey lines indicate scheduling. Detailed

description of the diagram: (i) Individual-level processes (rectangles) represented by females spring

( ) and autumn body masses ( ), allocation strategy ( and which again

influence the gain), summer metabolic rate ( ) and proportional winter mass loss ( ). (ii)

Population-level processes (circles) represented by summer population density ( ) and winter

environmental conditions ( ).

tjibmSpring,, tjibmAutumn

,,

jiS ,β

jiR , jiS ,

tD

t, tjiW ,,β

tE


0 50 100 150 200 250

-3

-2

-1

0

1

2

3 a) E ~ N(-0.15,0.5)

0 50 100 150 200 250

-3

-2

-1

0

1

2

3 b) E ~ N(-0.15,1)

0 50 100 150 200 250

-3

-2

-1

0

1

2

3 c) E ~ N(-0.15,1.5)

0 50 100 150 200 250

-3

-2

-1

0

1

2

3 d) E ~ N(0,0.5)

0 50 100 150 200 250

-3

-2

-1

0

1

2

3 e) E ~ N(0,1)

0 50 100 150 200 250

-3

-2

-1

0

1

2

3 f) E ~ N(0,1.5)

0 50 100 150 200 250

-3

-2

-1

0

1

2

3 g) E ~ N(0.15,0.5)

0 50 100 150 200 250

-3

-2

-1

0

1

2

3 h) E ~ N(0.15,1)

0 50 100 150 200 250

-3

-2

-1

0

1

2

3 i) E ~ N(0.15,1.5)

Time

Envi

ronm

ent (

E)

Figure A1.2. Simulated normally distributed environmental conditions (E). Realisation e) [E =

~N(0,1)] mimic the normalized principal components (PC) of climate indexes like AO and North

Atlantic Oscillation Index (NAO).


40 50 60 70 80 90 100 110

0.0

0.2

0.4

0.6

0.8

1.0

Spring female body mass (kg)

R

(a) Reproductive investment (R) b

0.08

0.08474

0.08947

0.09421

0.09895

0.10368

0.10842

0.11316

0.11789

0.122630.127370.132110.136840.141580.146320.151050.155790.160530.165260.17

0.08

0.10

0.120.14

0.16

4050

6070

8090

100

0.0

0.2

0.4

0.6

0.8

bSpring body mass

R

Figure A1.4. Female reproductive allocation ( ) as a function of spring body mass for dynamic state

dependent reproductive strategies. The relationship between reproductive allocation and spring body mass

( in eqn A2) is different for different strategies. Individuals will not invest in reproduction if their

spring body mass is below a threshold value (

R

Rb

springτ ). Note that the scale of the axis containing

spring body mass is different across figures.


10 20 30 40 50 60 70 80

0

20

40

60

Offspring mass development


Autu

mn

body

mas

s (k

g)

(a) Autumn offspring body mass (kg) Gain

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

0.5

Offspring mass development

0.00.2

0.40.6

0.81.0

20

40

60

80100

0

20

40

60

GainSpring (kg)

Autumn (kg)

10 20 30 40 50 60 70 80

0

20

40

60

80

100

Female mass development


Autu

mn

body

mas

s (k

g)

(b) Autumn female body mass (kg) Gain

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

0.5

Female mass development

0.00.2

0.40.6

0.81.0

20

40

60

80

100

0

20

40

60

80

100

GainSpring (kg)

Autumn (kg)

Figure A1.5. Summer mass development for offspring

(a) and female (b) as a function of gain (each line

representing different values for gain). Gain can be

interpreted as allocation in either reproduction (R;

offspring) or survival (S; female) within the limits set

by density and a summer metabolic rate (Table A1.2a;

Figure A1.6). The angle on the lines representing lines

with a gain <0.4 (a) is due to the fact that live

offspring are supposed to have an autumn body mass

above a threshold value ( autumn0 20 40 60 80 100 120

0

10

20

30

40

50

Body mass (BM measured in kg)

BMR

(mea

sure

d in

kg

stor

ed fa

t)

(c) Summer basal metabolic rate (BMR)

BMR = 0.4435 × BM

τ ). (c) Summer resting

metabolic rate as a function of spring body mass. Note

that the x-axis is different between the plots.


0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

R

Gai

n(a) Offspring gain Density

0.651.3

1.95

2.6

3.25

3.9

4.55

5.2

5.85

6.5

Offspring gain

01

23

45

6

0.0

0.2

0.4

0.60.8

1.00.0

0.2

0.4

0.6

0.8

1.0

DensityR

Gain

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

S

Gai

n

(b) Female gain Density

0.651.3

1.95

2.6

3.25

3.9

4.55

5.2

5.85

6.5

Female gain

01

23

45

6

0.0

0.2

0.4

0.60.8

1.00.0

0.2

0.4

0.6

0.8

1.0

DensityS

Gain

Figure A1.6. Gain in body mass for offspring (a) and female (b) as a function of allocation in either

reproduction (R; offspring) or survival (S; female) and density (different lines). The reward of a

fixed allocation will be limited by density; a fixed allocation will lead to lower gain at higher

compared to lower densities.


10 20 30 40 50 60 70

0.0

0.2

0.4

0.6

0.8

1.0

Offspring survival

Offspring autumn body mass (kg)

P(S

uviv

al |

fem

ale)

(a) Offspring winter survivalE

-2.86

-1.72

-0.570.57

1.72

2.86

Offspring winter survival

2030

4050

6070

-2-1

01

2

0.2

0.4

0.6

0.8

Autumn body mass (kg)E

P(Surv | female)

20 40 60 80 100

0.0

0.2

0.4

0.6

0.8

1.0

Female survival

Female autumn body mass (kg)

P(S

uviv

al |

fem

ale)

(b) Adult winter survival E

-2.86

-1.72

-0.57

0.57

1.72

2.86

Adult winter survival

2040

6080

100

-2-1

01

2

0.2

0.4

0.6

0.8

Autumn body mass (kg)E

P(Surv | female)

Figure A1.7. Over-winter survival as a function of autumn body mass and environmental

conditions for juveniles (a) and adult females (b). Note that the scales on the axes are different for

adult females and offspring.


-3 -2 -1 0 1 2 3

0.00

0.05

0.10

0.15

0.20

0.25

Functional form

Pro

porti

onal

loss

(a) Winter mass loss

+

-3 -2 -1 0 1 2 3

75

80

85

90

95

100

105

Autumn body mass = 100 (kg), n (per group) = 600

Spr

ing

body

mas

s (k

g) (b) Distribution: E ~ N(0,0.5)

75

80

85

90

95

100

105

-3 -2 -1 0 1 2 3

7580859095

100105110

Autumn body mass = 100 (kg), n (per group) = 600

Environmental conditions (E)

Spr

ing

body

mas

s (k

g) (c) Descriptive statistics: E ~ N(0,0.5)

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

0 0 0 0 0.01 0.01 0.01 0.020.03

0.030.04

0.040.03

0.020.02 0.01 0.01 0 0 0 0

Logistic relationship

Figure A1.8. (a) Proportional mean loss of (autumn) body mass as a function of environmental

conditions (line). Points are generated from the same model except that an error term is now also

included. Mean mass loss for E = 0 (marked with a cross) are taken from the literature (Table

A1.2d). (b) A boxplot showing the distribution (median, 75% and 25% quartiles and outlying

observations as points) for 600 constant autumn masses. (c) Descriptive statistics, i.e. means with

standard deviations (bars) and coefficient of variations (text), for several environmental values

(groups) using the same realisation as in the previous plot (see Table A1.2d for details).


Table A1.1. Values used for the initiation of the model. Parameter Explanation Value (scale) Source/Notes

(a) Initiation (Figure A1.2-A1.4 & Expression A1-A5)

0t Initial time (spring) 0 (year) ______

A Study area 2000 (km2) ______

0t

n Number of females present at 0t 800 (number) ______

stratn The number of different strategies at 0t 40 (number) ______ a

stratt nn0

The number of individuals within each strategy stratum at 0t

20 (number) ______

70.60=x (kg)

itbmSpring

,0

Initial spring body mass generated from a normally distribution with a given mean ( x )

and standard deviation ( ): y ( )yxN ,≈ 00.5=y (kg) (Fauchald et al. 2004: Table

2b)b,c

0t

j Initial age similar for all individuals 2 (year) (Crête et al. 1994, Fancy et al. 1994, Albon et al. 2002)

maxj Maximum (max) possible age 16 (year) Personal communicationd

springτ Reproductive spring mass threshold in the dynamic state dependent strategy (DSDS) 43.20 (kg) Tveraa et. al (unpul. data)e

Ra Intercept in the equation defining the DSDS -10.00 (constant) ______

minRb Minimum (min) slope ( R ) in the equation defining the DSDS

b 0.08 (constant) ______

maxRb Max slope ( ) in the equation defining the DSDS

Rb 0.17 (constant) ______

a This gives rise to 20 fixed (equally spaced reproductive allocation strategies between 0 and 1) and 20 dynamic state dependent strategies (equally spaced values of between and ). Rb minRb maxRb

b These estimate is based on subtracting the reported body masses for a female on natural pasture with the mean body mass of a newborn calf of 7.8 kg (their Table 2).

c The standard deviation is found by comparing the reported quartilesb in Fauchald et al. (2004) with a generated normal distribution using their mean valueb following function

quantile(rnorm(mean = 68.5-7.8, sd = x, n = 1000))[c(2, 4)] in the software R (R Development Core Team 2007). By testing different values of x we found that x

= 5 gave approximately similar quartiles as reported by Fauchald et al. (2004).

d Heikki Törmänen, Reindeer Research Station, Finnish Game and Fisheries Research Institute, Kaamanen, Finland: data from 1993, experimental reindeer herd in Kutuharju, Finland.

e T. Tveraa, P. Fauchald, K. Langeland & B.-J. Bårdsen: data from 16C (a reindeer herding district in Finnmark, Northern Norway), collected on the 24th of May 2003.


Table A1.2. Parameters used in the model. Parameter Explanation Value (scale) Source/Notes

(a) Autumn body mass (Figure A1.5 & Expression A6-A11, A15-A16)

tibmBirth

, Mean birth mass ( 1<j ) 7.8 (kg) (Valkenburg et al. 2003,

Adams 2005)

Threshold for min. mass: offspring ( 1<j ) 15.0 (kg) ______

jautumnτ

female ( ) 1≥j 15.0 (kg) ______

tjibmSpring

,, Spring body mass ( ) 1≥j Estimate (kg) ______

Threshold for max. mass: offspring ( 1<j ) 73.0 (kg) Personal communicationa

jbmτ

female ( ) 1≥j 103.0 (kg) (Holand et al. 2004)

βa Intercept for summer basal metabolic rate 0.000 (constant)

( )( )0

0

2

max

−

−=

=jbm

sbτ

ββ Constant for spring body mass 0.628 (constant)

(Nilssen et al. 1984, Schmidt-Nielsen 1997)c

(b) Gain (Figure A1.6 & Expression A12-A13)

tD Density; Ant Estimate (n km-2) (Tveraa et al. 2007)d

Gb Constant for allocation: or jiS , jiR , 1.000 (constant) ______

Gc Constant for density -0.150 (constant) ______

Gd Constant for interaction -0.140 (constant) ______

a Heikki Törmänen, Reindeer Research Station, Finnish Game and Fisheries Research Institute, Kaamanen, Finland: data from the experimental reindeer herd in Kutuharju, Finland.

b This is based on the lowest autumn (December) female reindeer dressed body mass in Reimers (1983b: Figure 2). In order to ‘transform’ dressed body mass it into live mass we multiplied the

dressed body mass by 1.92 as suggested by Reimers (1983a).

c This is based on a summer basal metabolic rate (BMR) of 2.36 W (J s-1) kg-1 for Norwegian and Svalbard reindeer (Nilssen et al. 1984: average summer and autumn resting metabolic rates

presented in their Table 1). Total summer BMR was calculated on a daily basis, i.e. assuming a constant daily BMR, summed over 184 days (length of the summer season). Total summer BMR

was based on spring body mass, i.e. birth mass for offspring, as starting conditions. Maximum possible summer BMR ( ) is the summer BMR for the largest possible female body mass

(defined by ). Daily BMR was estimated according to well-known physiological relationships and by converting Joule (J) to calories using the following constants: 1 J = 0.239 cal, 1 kcal

= 1000 cal & 1 kcal = 0.1011 g or 0.00011 kg stored fat (Schmidt-Nielsen 1997).

maxsβ

2=jbmτ

d Maximum density, which limits the gain function (gain will then be zero), is set to 6.5 individuals km-2 (Tveraa et al. 2007: Figure 4a).


Table A1.2. Continued. Parameter Explanation Value (scale) Source/Notes

(c) Winter survival (Figure A1.7 & Expression A16)

Asymptote for survival; offspring ( 1<j ) 0.954 (prob.) (Rødven 2003)e

jWI

female ( ) 1≥j 0.990 (prob.) (Albon et al. 2002)e

Intercept: offspring ( 1<j ) -5.750 (constant)

jWa

female ( ) 1≥j -5.750 (constant) ______ f

Constant for autumn mass: offspring ( 1<j ) 0.125 (constant)

Wjb

female ( ) 1≥j 0.110 (constant) ______ f

Constant for environment: offspring ( 1<j ) -0.225 (constant)

Wjc


Constant for interaction: offspring ( 1<j ) -0.025 (constant)

Wjd


(d) Spring body mass (Figure A1.8 & Expression A17-A18)

LossI Max. proportional body mass loss

(converted from proportional to logitg scale) 0.260 (prop.) (Bergerud 1974, Dauphiné 1976, Bradshaw et al. 1998)

tjie ,, error term: ( )xN ,0≈ 0.500 (logit) ______

Lossϑ Scaling parameter used when estimating

Lossa 0.005 (prop.) ______

minE / maxE Max./min. environmental value -2.860/2.860 Mimics AOh

( )[ ]21logit WLossa ϑ−= Intercept Estimate (logit) (Bradshaw et al. 1998 and referenced therein)i

( ) ( )[ ]( )minmax

logit1logitEE

b WWLoss −

−−=

ϑϑ Constant for environment Estimate (logit) ______ j

e The upper 95% confidence interval (CI) for prime-aged survival is taken as asymptote for adults (Albon et al. 2002), whereas the we estimated this from the maximum yearly mean (1.60 on logit

f Th o juvenile survival, which is highly variable (reviewed by e.g. Gaillard et al. 2000). Different

g Logit, or log-odds

scale) and 0.74 standard error (SE) for survival 4-16 months from Rødven (2003: his table 3).

e general finding in the literature is that adult female survival varies little from year-to-year relative t

coefficients for the two age classed are chosen to take this into account (Figure A1.7). However, even adult survival has been found to decrease for reindeer experiencing extreme winter

conditions (Tveraa et al. 2003). Thus, during extreme environmental conditions even adult survival will be affected in this model (Figure A1.7b).

of proportions/probabilities, of x is defined as: ( ) ( )xxx −= 1loglogit . The antilogit, i.e. transformation from logit to proportion/probability scale, is defined as:

( ) ( )[ ]xeIx 111antilogit +×= , where the asymptotic value ( I ) usua

.ucar.edu/cas/jhurrell/indices.data.html#nam

lly is set to 1.

h Based on data available at http://www.cgd . The minimum/maximum is the maximum absolute value of normalized PC values of the annual Artic

i Aver age year (E = 0)

on a probability s

Oscillation Index from 1899 until 2007). The minimum and maximum values must be symmetrical as the estimated intercept will be wrong if unsymmetrical values are chosen.

age loss of autumn body mass during winter for Rangifer tarandus have been reported to be 12.5% (Bradshaw et al. 1998). Thus, we tuned the models so that (i) during an aver

average loss of body reserves is ~0.125, (ii) at an extremely god year (E = -2.85) average loss is ~0 and (iii) during an extremely harsh year (E = 2.85) loss is ~0.26 on average (Bergerud 1974).

nsures that mass loss goes towards zero (spring mass ~ autumn mass) for extremely god years (as E goes towards -2.85) and towards or extremely bad years (as E goes towards 2.85) jLossI e LossI f

ion arcale (0 and are the asymptotes in the logistic relationships). The intercept, slope, and st. dev. are logits as all calculat e performed on logit scale. LossI

Plastic reproductive allocation and environmental unpredictability

A2.1

A2: FIGURE OF IMPORTANT OUTPUT AS A FUNCTION OF

TIME FOR THE STANDARD NORMALLY DISTRIBUTED

ENVIRONMENT

Important output of details associated with one example simulation (Figure A2.1).

Plastic reproductive allocation and environmental unpredictability

A2.2

0 100 200 300 400

-3

-2

-1

0

1

2

3 (a)

Envi

ronm

ent (

rela

tive)

0 100 200 300 400

0.2

0.4

0.6

0.8

1.0

1.2(b)

Den

sity

(ind

. km

−2)

0 100 200 300 400

-1.06

-0.70

-0.35

0.01

0.36

r

0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8

1.0

Prop

rotio

n

27(c)

0 5 10 15 20

0

20

40

60

80

100 (d)

Mea

n fe

mal

e bo

dy m

ass

(kg)

0

20

40

60

80

100

450 455 460 465

0 5 10 15 20

0

20

40

60

(e)

Mea

n of

fspr

ing

body

mas

s (k

g)

0

20

40

60

-

450 455 460 465

-0.011

0.009

0.117

0.013

0.03

0.096

0.105

0.0240.044

0.068

0.019

0.159

0.012

0.0010.003

0.051

0.0150.04

0.107

0.007

Simulation results [mean(E) = 0, sd(E) = 1]

Time (years)

Figure A2. Distribution of (a) winter climatic conditions, (b) population density and growth rates

and (c) proportion of individuals in each reproductive investment strategy (blue represent DSDS

and red represents FS) from start ( ) to the end of the simulation (0tt = Tt = ). (d) Average female

body mass for the first ( to ; blue) and last 20 years (0t 20=t 20−= Tt to Tt = ; red). Grey lines

represent the average body mass for each strategy present within the first 20 years. (e) Shows the

same as figure d except that this shows the same trend for offspring body mass. Numbers for the

red labelled line indicated the proportion of females breeding successfully within each year.


A3: TERMINAL TIME AND A TEST OF THE DESIGN:

ENVIRONMENTAL INPUT VALUES

The relationship between terminal time (T ) and estimated distributional parameters of the two

input variables; i.e. the theoretic average (x) and the theoretic standard deviation (y) for

environmental conditions (Table A3.1). These results are based on data from the 60 years

preceding T .


Table A3.1. Estimates from linear models (LM) relating final time (a), environmental average and

(b) as well as (c) environmental stochasticity to the theoretic input values for the environment

[theoretical averages ( ) and theoretical standard deviations (x y )]. The intercept shows average

body mass for; (1) the level ‘Control’ for the factor environmental conditions. The other

coefficients are the estimated difference between the intercept, or the main effect for y , for each

level of the other included factors.


(a) Terminal time ( T )

Intercept 1120.32 (873.72, 1366.92) 9.03 <0.01

Average environment (x) [Improved] -539.74 (-886.38, -193.09) -3.10 <0.01

Average environment (x) [Reduced] -902.75 (-1261.39, -544.12) -5.01 <0.01

Standard deviation for environment (y) -473.13 (-754.63, -191.63) -3.34 <0.01

x [Improved] × y 421.89 (31.79, 811.99) 2.15 0.03

x [Reduced] × y 926.92 (487.03, 1366.81) 4.19 <0.01

R2 = 0.25, F5,84 = 5.49, P < 0.01 (b) Environmental average ( E )

Intercept -0.01 (-0.04, 0.04) -0.07 0.93

x [Improved] -0.14 (-0.20, -0.08) -4.68 <0.01

x [Reduced] 0.11 (0.05, 0.17) 3.57 <0.01

R2 = 0.44, F5,87 = 33.29, P < 0.01 (c) Environmental stochasticity [ ] ( )E dev. st.

Intercept -0.01 (-0.03, 0.03) -0.09 0.93

y 1.01 (0.97, 1.04) 58.42 <0.01

R2 = 0.98, F5,87 = 3413.00, P < 0.01

Risk sensitive reproductive strategies - nina.no¥rdsen Risk... · Krebs 1986, Kacelnik and Bateson...

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